TWI732351B - Tube flow rate measurement system and method thereof - Google Patents

Tube flow rate measurement system and method thereof Download PDF

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TWI732351B
TWI732351B TW108142158A TW108142158A TWI732351B TW I732351 B TWI732351 B TW I732351B TW 108142158 A TW108142158 A TW 108142158A TW 108142158 A TW108142158 A TW 108142158A TW I732351 B TWI732351 B TW I732351B
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flow
pipeline
sensor group
flow rate
correction coefficient
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TW202120892A (en
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蔡明倫
林昆民
林鴻文
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財團法人工業技術研究院
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Abstract

A tube flow rate measurement system is configured to measure a fluid flow rate of a fluid passing through a test segment of a tube, and the fluid flow rate measurement system comprises a first sensor set, a second sensor set, and a computing device. The first sensor set and the second sensor set are respectively configured to connect with two ends of the test segment, and the computing device is electrically connected to the first sensor set and the second sensor set. The computing device calculates a fluid velocity set according to a plurality of sensing signal pairs transmitted between the first sensor set and the second sensor set, and the computing device stores a plurality of classifications which is generated by executing a supervised learning many times and a fluid flow rate correction coefficient database. The computing device determines a flow field type of the fluid velocity set according to the classifications, and obtains a fluid flow rate correction coefficient corresponding to the flow field type of the fluid velocity set from the fluid flow rate correction coefficient database, and calculate the fluid flow rate according to the fluid flow rate correction coefficient and the fluid velocity set.

Description

管路流量量測系統及其方法Pipeline flow measurement system and method

本發明係關於一種管路內流體的流量之量測系統及其量測方法。 The invention relates to a measuring system and a measuring method for the flow of fluid in a pipeline.

目前的中央空調系統由於涉及多種設備之間的熱傳遞、水量、風量、冷媒量之調控,若多種設備之間的運轉協調不良,將出現電能虛耗之情形。中央空調系統的各種設備之中,以水側系統(water-side system)的耗電量最大,因此水側系統的效能對於中央空調系統的節能效率有決定性影響。水側系統包含冰水主機、冰水泵與冷卻水塔,其中水側系統的運作效能通常以kW/RT為判斷基準,其中kW為水側系統的總耗電量,而RT為依據冰水流量以及冰水進出口溫差所計算出的供應冷凍噸。當kW/RT的數值愈小,即表示水側系統的效能愈佳,進而影響中央空調系統的節能效率。 The current central air-conditioning system involves the regulation of heat transfer, water volume, air volume, and refrigerant volume between multiple devices. If the operation of multiple devices is poorly coordinated, electrical energy will be wasted. Among the various equipment of the central air-conditioning system, the water-side system consumes the most power. Therefore, the efficiency of the water-side system has a decisive influence on the energy-saving efficiency of the central air-conditioning system. The water-side system includes an ice water main engine, an ice water pump, and a cooling water tower. The operating performance of the water-side system is usually judged based on kW/RT, where kW is the total power consumption of the water-side system, and RT is based on the flow of ice water and Supply refrigerated tons calculated from the temperature difference between the inlet and outlet of ice water. When the value of kW/RT is smaller, it means that the efficiency of the water side system is better, which in turn affects the energy-saving efficiency of the central air conditioning system.

由於水側系統的管路設計越來越複雜,造成許多長度較短的管路內的流體無法形成完全發展流(fully developed flow),而目前的流量量測技術對於非完全發展流(non-fully developed flow)的流量之量測,誤差甚至可達10%,導致無法準確量測中央空調水側系統的效能,進而造成節能改善措施不易執行及難以驗證成效。目前國內的商辦建築通常都採用中央空調系統,使得中央空調系統之耗電為國內用電的最大宗,因應目前電廠發電經常超載的問題,實有必要精確地控管水側系統之流量及效能,以達到節能減碳的效果。 As the piping design of the water-side system is becoming more and more complex, the fluid in many short-length pipes cannot form a fully developed flow. However, the current flow measurement technology is not suitable for non-fully developed flow. The error of the fully developed flow measurement can even reach 10%, which makes it impossible to accurately measure the performance of the central air-conditioning water-side system, which makes it difficult to implement energy-saving improvement measures and difficult to verify the effectiveness. At present, domestic commercial and office buildings usually use central air-conditioning systems, making the power consumption of central air-conditioning systems the largest domestic electricity consumption. In response to the current problem of frequent overloading of power generation in power plants, it is necessary to accurately control the flow and flow of water-side systems. Efficiency to achieve the effect of energy saving and carbon reduction.

本發明提供一種管路流量量測系統及其方法,無論管路內的流體屬於非完全發展流或完全發展流,都可精確地量測到管路內的流體的流量,進而達到節能減碳的效果。 The present invention provides a pipeline flow measurement system and method. Regardless of whether the fluid in the pipeline belongs to an incompletely developed flow or a fully developed flow, the flow of the fluid in the pipeline can be accurately measured, thereby achieving energy saving and carbon reduction Effect.

本發明所揭露的一種管路流量量測系統,其用於量測管路的待測段內的流體的流量,該管路流量量測系統包括第一感測器組、第二感測器組以及運算裝置,第一感測器組及第二感測器組分別用於組接於待測段的相異二端,而運算裝置電性連接於第一感測器組以及第二感測器組。運算裝置依據傳輸於第一感測器組及第二感測器組之間的多筆感測訊號對來計算一流速組合,且儲存透過執行多次監督式學習而產生的多個分類演算法及流量修正係數資料庫。運算裝置依據該些分類演算法以判斷該流速組合所屬於的流場種類、從流量修正係數資料庫取得對應流場種類的流量修正係數、以及依據流量修正係數以及該流速組合以計算流體之流量。 A pipeline flow measurement system disclosed in the present invention is used to measure the flow of fluid in a section to be measured of a pipeline. The pipeline flow measurement system includes a first sensor group and a second sensor The first sensor group and the second sensor group are respectively used to connect to two different ends of the segment to be measured, and the computing device is electrically connected to the first sensor group and the second sensor group. Detector group. The arithmetic device calculates a flow rate combination based on the multiple sensor signal pairs transmitted between the first sensor group and the second sensor group, and stores multiple classification algorithms generated by performing multiple supervised learning And flow correction coefficient database. The computing device determines the flow field type to which the flow velocity combination belongs according to the classification algorithms, obtains the flow correction coefficient corresponding to the flow field type from the flow correction coefficient database, and calculates the flow rate of the fluid based on the flow correction coefficient and the flow velocity combination .

本發明所揭露的一種量測管路流量的方法,其用於量測管路的待測段內的流體的流量,包括:以運算裝置讀取傳輸於第一感測器組及第二感測器組之間的多筆感測訊號對;以運算裝置依據該些感測訊號對以計算流體的一流速組合,其中運算裝置儲存有透過執行多次監督式學習而產生的多個分類演算法及流量修正係數資料庫;以該些分類演算法判斷該流速組合所屬於的流場種類;以流場種類從流量修正係數資料庫取得對應流場種類的流量修正係數;以及以運算裝置依據該流速組合與流量修正係數計算流體之流量。 The present invention discloses a method for measuring the flow rate of a pipeline, which is used to measure the flow rate of a fluid in a section to be measured of a pipeline, including: reading and transmitting to a first sensor group and a second sensor by an arithmetic device The multiple sensing signal pairs between the sensor groups; the calculation device calculates a flow rate combination of the fluid according to the sense signal pairs, wherein the calculation device stores multiple classification calculations generated by performing multiple supervised learning Method and flow correction coefficient database; use these classification algorithms to determine the flow field type to which the flow rate combination belongs; use the flow field type to obtain the flow correction coefficient corresponding to the flow field type from the flow correction coefficient database; and use the calculation device to base it The flow rate is combined with the flow correction coefficient to calculate the flow rate of the fluid.

本發明所揭露的管路流量量測系統及量測管路流量的方法,舉例透過多次執行屬於監督式學習的支持向量機所產生的多個不同的分類演算法,即便管路內的流體屬於非完全發展流,也可準確地依據該些超平面方程式判斷該流體所屬於的流場種類,以便依據流場種類從修正係數資料庫中取得合適的流量修正係數。如此一來,運算裝置便可依據流體的流 速資料去精確地判斷流體所屬於的流場種類,依據流場種類找出對應的流量修正係數,依據流量修正係數計算出更精確的流體流量、依據精確的流量值可有效率地監控水側系統的效能,進而達到節能減碳的效果。 The pipeline flow measurement system and the method for measuring pipeline flow disclosed in the present invention, for example, through multiple executions of multiple different classification algorithms generated by a support vector machine belonging to supervised learning, even if the fluid in the pipeline If it belongs to an incompletely developed flow, the flow field type of the fluid can also be accurately determined according to the hyperplane equations, so as to obtain an appropriate flow correction coefficient from the correction coefficient database according to the flow field type. In this way, the arithmetic device can be based on the flow of the fluid Speed data to accurately determine the type of flow field the fluid belongs to, find out the corresponding flow correction coefficient based on the flow field type, calculate more accurate fluid flow based on the flow correction coefficient, and effectively monitor the water side based on the accurate flow value The efficiency of the system, in turn, achieves the effect of energy saving and carbon reduction.

以上之關於本揭露內容之說明及以下之實施方式之說明係用以示範與解釋本發明之精神與原理,並且提供本發明之專利申請範圍更進一步之解釋。 The above description of the disclosure and the following description of the embodiments are used to demonstrate and explain the spirit and principle of the present invention, and to provide a further explanation of the scope of the patent application of the present invention.

11:第一感測器組 11: The first sensor group

111~114:第一感測器 111~114: The first sensor

12:第二感測器組 12: The second sensor group

121~124:第二感測器 121~124: second sensor

13:運算裝置 13: Computing device

131:處理器 131: Processor

132:記憶體 132: Memory

1321:流場種類分類資料庫 1321: Classification database of flow field types

1322:流量修正係數資料庫 1322: Flow correction coefficient database

133:控制器 133: Controller

134:輸入操作介面 134: Input operation interface

T:管路 T: Pipeline

T1:待測段 T1: segment to be tested

Ex:入口端 Ex: Entry side

En:出口端 En: export side

P1~P8:第一位置至第八位置 P1~P8: the first position to the eighth position

L:中心軸 L: central axis

N:截面 N: cross section

C1~C16:量測路徑 C1~C16: Measurement path

HP1:第一超平面 HP1: the first hyperplane

HP2:第二超平面 HP2: second hyperplane

V1:第一流速 V1: First flow rate

V2:第二流速 V2: Second flow rate

f1:第一流場 f1: the first flow field

f2:第二流場 f2: second flow field

f3:第三流場 f3: third flow field

圖1係繪示本發明所揭露的管路流量量測系統的第一實施例的功能方塊圖。 FIG. 1 is a functional block diagram of the first embodiment of the pipeline flow measurement system disclosed in the present invention.

圖2係繪示本發明所揭露的管路流量量測系統應用於管路的第一實施態樣的示意圖。 2 is a schematic diagram showing a first embodiment of the pipeline flow measurement system disclosed in the present invention applied to pipelines.

圖3係繪示圖2的另一視角的示意圖。 FIG. 3 is a schematic diagram of FIG. 2 from another perspective.

圖4係繪示本發明所揭露的管路流量量測系統應用於管路的第二實施態樣的示意圖。 4 is a schematic diagram showing a second embodiment of the pipeline flow measurement system disclosed in the present invention applied to pipelines.

圖5係繪示本發明所揭露的管路流量量測系統應用於管路的第三實施態樣的示意圖。 FIG. 5 is a schematic diagram showing a third embodiment of the pipeline flow measurement system disclosed in the present invention applied to pipelines.

圖6係繪示本發明所揭露的量測管路流量的方法的一實施例的方法流程圖。 FIG. 6 is a method flowchart of an embodiment of the method for measuring pipeline flow rate disclosed in the present invention.

圖7係繪示圖6所揭露的判斷管路的流體所屬於的流場種類的詳細流程圖。 FIG. 7 is a detailed flowchart of determining the type of flow field of the fluid in the pipeline disclosed in FIG. 6.

圖8係繪示圖6所揭露的判斷管路的流體所屬於的流場種類的示意圖。 FIG. 8 is a schematic diagram illustrating the type of flow field to which the fluid in the pipeline belongs to the fluid in the pipeline disclosed in FIG. 6.

圖9係繪示本發明建立流量修正係數的一實施例的方法流程圖。 FIG. 9 is a flowchart of a method for establishing a flow correction coefficient according to an embodiment of the present invention.

圖10係繪示本發明執行機器學習程序以建立流場種類分類資料庫的一實施例的方法流程圖。 FIG. 10 is a flowchart of an embodiment of the present invention executing a machine learning program to build a flow field classification database.

以下在實施方式中詳細敘述本發明之詳細特徵以及優點,其內容足以使任何熟習相關技藝者了解本發明之技術內容並據以實施,且根據本說明書所揭露之內容、申請專利範圍及圖式,任何熟習相關技藝者可輕易地理解本發明相關之目的及優點。以下之實施例係進一步詳細說明本發明之觀點,但非以任何觀點限制本發明之範疇。 The detailed features and advantages of the present invention will be described in detail in the following embodiments. The content is sufficient to enable anyone familiar with the relevant art to understand the technical content of the present invention and implement it accordingly, and according to the content disclosed in this specification, the scope of patent application and the drawings. Anyone who is familiar with relevant skills can easily understand the purpose and advantages of the present invention. The following examples further illustrate the viewpoints of the present invention in detail, but do not limit the scope of the present invention by any viewpoint.

圖1係繪示本發明所揭露的管路流量量測系統之第一實施例的功能方塊圖。如圖1所示,管路流量量測系統包括一第一感測器組11、一第二感測器組12以及一運算裝置13,而運算裝置13電性連接於第一感測器組11以及第二感測器組12。運算裝置13例如為雲端主機、伺服器或行動通訊裝置,運算裝置包含一處理器131、一記憶體132、一控制器133以及一輸入操作介面134,而處理器131電性連接於記憶體132、控制器133以及輸入操作介面134。記憶體132儲存有多個一流場種類分類資料庫1321及一個流量修正係數資料庫1322,其中流場種類分類資料庫1321包含經由多次執行監督式學習(Supervised Learning)而產生的多個分類演算法(Classification),而該些分類演算法用於分類多個不同的流場種類,而流量修正係數資料庫1321包含多個不同的流場種類以及對應於該些流場種類的多個不同的流量修正係數。在本實施例中,監督式學習舉例為一支持向量機(support vector machine),每執行一次支持向量機可產生一個超平面方程式以分類出兩種流場種類,藉由多次執行支持向量機以產生多個不同的超平面方程式(hyperplane equation)而可分類出多個兩種的流場種類。舉例來說,流場種類分類資料庫1321包含由執行支持向量機而產生的第一超平面方程式以及第二超平面方程式,第一超平面方程式用於判斷流體模型是否屬於A流場,第二超平面方程式用於判斷流場模型是否屬於B流場。流量修正係數資料庫1322包含有流場A及其對應的流量修正係數D1(例如1.0)、以及流場B以其對應的流量修正係數D2(例如0.955)。 FIG. 1 is a functional block diagram of the first embodiment of the pipeline flow measurement system disclosed in the present invention. As shown in FIG. 1, the pipeline flow measurement system includes a first sensor group 11, a second sensor group 12, and an arithmetic device 13, and the arithmetic device 13 is electrically connected to the first sensor group 11 and the second sensor group 12. The computing device 13 is, for example, a cloud host, a server, or a mobile communication device. The computing device includes a processor 131, a memory 132, a controller 133, and an input operation interface 134, and the processor 131 is electrically connected to the memory 132 , A controller 133 and an input operation interface 134. The memory 132 stores a plurality of first-class field classification databases 1321 and a flow correction coefficient database 1322. The flow field classification database 1321 includes multiple classification calculations generated by performing supervised learning multiple times. The classification algorithm is used to classify a plurality of different flow field types, and the flow correction coefficient database 1321 contains a plurality of different flow field types and a plurality of different flow field types corresponding to the flow field types. Flow correction factor. In this embodiment, the supervised learning is an example of a support vector machine. Each time the support vector machine is executed, a hyperplane equation can be generated to classify two flow field types. By executing the support vector machine multiple times A plurality of different hyperplane equations (hyperplane equations) can be generated to classify a plurality of two kinds of flow field types. For example, the flow field classification database 1321 includes a first hyperplane equation and a second hyperplane equation generated by the execution of a support vector machine. The first hyperplane equation is used to determine whether the fluid model belongs to the flow field A, and the second hyperplane equation is used to determine whether the fluid model belongs to the flow field A. The hyperplane equation is used to determine whether the flow field model belongs to the B flow field. The flow correction coefficient database 1322 includes flow field A and its corresponding flow correction coefficient D1 (for example, 1.0), and flow field B and its corresponding flow correction coefficient D2 (for example, 0.955).

使用者透過輸入操作介面134輸入一啟動指令,接著輸入操作介面134將傳送該啟動指令至處理器131,而處理器131傳送啟動指令至控制器133,而控制器133依據該啟動指令以致能第一感測器組11以及第二感測器組12,如此一來,第一感測器組11以及第二感測器組12便可感測管路內流體的狀態以產生感測訊號,並傳送感測訊號至控制器133,控制器133再傳輸感測訊號至處理器131以進行後續流量計算。 The user inputs a start command through the input operation interface 134, and then the input operation interface 134 will send the start command to the processor 131, and the processor 131 sends the start command to the controller 133, and the controller 133 enables the first command according to the start command. A sensor group 11 and a second sensor group 12, in this way, the first sensor group 11 and the second sensor group 12 can sense the state of the fluid in the pipeline to generate a sensing signal, The sensing signal is sent to the controller 133, and the controller 133 transmits the sensing signal to the processor 131 for subsequent flow calculation.

圖2係繪示本發明所揭露的管路流量量測系統應用於管路的第一實施態樣的示意圖,而圖3係繪示圖2的另一視角的示意圖。如圖2所示,管路流量量測系統用於量測管路T的待測段內的流體的流量,其中待測段可為管路T或者管路T的一部份。在本實施例中,待測段為管路T,所以待測段的相異兩端分別為管路T的入口端Ex以及出口端En,而該第一感測器組11以及該第二感測器組12分別組接於管路T的入口端Ex以及出口端En。 FIG. 2 is a schematic diagram of a first embodiment of the pipeline flow measurement system disclosed in the present invention applied to a pipeline, and FIG. 3 is a schematic diagram of FIG. 2 from another perspective. As shown in FIG. 2, the pipeline flow measurement system is used to measure the flow of fluid in the section to be measured of the pipeline T, where the section to be measured can be the pipeline T or a part of the pipeline T. In this embodiment, the section to be measured is the pipeline T, so the different ends of the section to be measured are the inlet end Ex and the outlet end En of the pipeline T, and the first sensor group 11 and the second sensor group 11 The sensor group 12 is connected to the inlet end Ex and the outlet end En of the pipeline T, respectively.

完全發展流的流體的流速分佈均勻,僅需要一筆流速資料即可正確地表示流體的實際狀態。然而非完全發展流的流速分佈不均勻,一筆流速資料無法正確地表示流體的實際狀態,必須依據多筆依據流速資料才能正確地表示流體的實際狀態。為了正確地表示非完全發展流的流體的實際狀態,必須於管路上設置足夠數量的感測器。在本實施例中,該第一感測器組11包含多個第一感測器111~114,該第二感測器組12包含多個第二感測器121~124。在本實施例中,該些第一感測器111~114以及該些第二感測器121~124均為超音波感測器。管路T的入口端Ex設有第一位置至第四位置P1~P4,而該第一位置至該第四位置P1~P4彼此之間的間距相等且位於管路T的外部,而該些第一感測器111~114分別組接於第一位置至第四位置P1~P4。管路T的出口端En設有第五位置至第八位置P5~P8,而該第五位置至該第八位置P5~P8彼此之間的間距相等且第五位置至第八位置P5~P8位於管路T的外部,而該些第二感測器121~124分別組接於 第五位置至第八位置P5~P8。管路T定義一中心軸L以及通過該中心軸L的一截面N,而中心軸L位於截面N上。該些第一感測器111~114位於截面N的左側,而該些第二感測器121~124位於截面N的右側。記憶體132內更儲存有權重組合,其中該權重組合關連於該第一感測器組11以及該第二感測器組12於管路T的設置位置以及管路T的徑長。 The flow velocity of a fully developed fluid is evenly distributed, and only one flow velocity data is needed to accurately represent the actual state of the fluid. However, the flow velocity distribution of the incompletely developed flow is not uniform. One flow velocity data cannot accurately represent the actual state of the fluid, and multiple flow velocity data must be used to correctly represent the actual state of the fluid. In order to accurately represent the actual state of the incompletely developed fluid, a sufficient number of sensors must be installed on the pipeline. In this embodiment, the first sensor group 11 includes a plurality of first sensors 111 to 114, and the second sensor group 12 includes a plurality of second sensors 121 to 124. In this embodiment, the first sensors 111 to 114 and the second sensors 121 to 124 are ultrasonic sensors. The inlet end Ex of the pipeline T is provided with a first position to a fourth position P1~P4, and the distance between the first position to the fourth position P1~P4 is equal to each other and is located outside the pipeline T, and these The first sensors 111-114 are respectively assembled in the first position to the fourth position P1 to P4. The outlet end En of the pipeline T is provided with the fifth position to the eighth position P5~P8, and the distance between the fifth position to the eighth position P5~P8 is equal, and the fifth position to the eighth position P5~P8 Located outside the pipeline T, and the second sensors 121~124 are respectively assembled to The fifth position to the eighth position P5~P8. The pipeline T defines a central axis L and a section N passing through the central axis L, and the central axis L is located on the section N. The first sensors 111 to 114 are located on the left side of the section N, and the second sensors 121 to 124 are located on the right side of the section N. The memory 132 further stores a weighted combination, wherein the weighted combination is related to the arrangement positions of the first sensor group 11 and the second sensor group 12 in the pipeline T and the diameter of the pipeline T.

當第一感測器組11作為訊號發送端,同一時間只有一個第一感測器發送感測訊號,而可由該些第二感測器接收。當該第二感測器組12作為訊號發送端,同一時間下僅有一個第二感測器發送感測訊號,而可由該些第一感測器接收。如圖3所示,第一感測器111與該些第二感測器121~124之間具有不同的量測路徑C1~C4,第一感測器112與該些第二感測器121~124之間具有不同的量測路徑C5~C8,第一感測器113與該些第二感測器121~124之間具有不同的量測路徑C9~C12,而第一感測器114與該些第二感測器121~124之間具有不同的量測路徑C13~C16。舉例而言,當第一感測器111發送第一感測訊號時,其他第一感測器112~114不會發送任何感測訊號,且由該些第二感測器121~124分別經由量測路徑c1~c4接收第一感測訊號。當第二感測器121發送第二感測訊號時,其他第二感測器122~124不會發送第二感測訊號,且由該些第一感測器111~114分別經由量測路徑C1、C5、C9及C13接收第二感測訊號。傳送於同一量測路徑(例如C1)上的一個第一感測訊號以及一個第二感測訊號定義為一個感測訊號對,在本實施例中,第一感測器與第二感測器各具有四個,所以可形成16筆感測訊號對。藉此,處理器131依據傳輸於第一感測器組11及第二感測器組12之間的16筆感測訊號對計算出一流速組合,而該流速組合包含有16筆流速資料,而處理器131用於計算流速v的公式推導如下:c-vcos θ=L/t1 (式1)。 When the first sensor group 11 is used as a signal sending end, only one first sensor sends a sensing signal at the same time, which can be received by the second sensors. When the second sensor group 12 is used as a signal transmitter, only one second sensor sends a sensing signal at the same time, which can be received by the first sensors. As shown in FIG. 3, there are different measurement paths C1 to C4 between the first sensor 111 and the second sensors 121 to 124, and the first sensor 112 and the second sensors 121 There are different measurement paths C5~C8 between ~124, the first sensor 113 and the second sensors 121~124 have different measurement paths C9~C12, and the first sensor 114 There are different measurement paths C13 to C16 between the second sensors 121 to 124. For example, when the first sensor 111 sends the first sensing signal, the other first sensors 112 to 114 will not send any sensing signal, and the second sensors 121 to 124 respectively pass through The measurement paths c1~c4 receive the first sensing signal. When the second sensor 121 transmits the second sensing signal, the other second sensors 122 to 124 do not transmit the second sensing signal, and the first sensors 111 to 114 respectively pass the measurement path C1, C5, C9 and C13 receive the second sensing signal. A first sensing signal and a second sensing signal transmitted on the same measurement path (such as C1) are defined as a sensing signal pair. In this embodiment, the first sensor and the second sensor Each has four, so 16 sensing signal pairs can be formed. In this way, the processor 131 calculates a flow rate combination based on 16 pairs of sensing signals transmitted between the first sensor group 11 and the second sensor group 12, and the flow rate combination includes 16 flow rate data. The formula used by the processor 131 to calculate the flow velocity v is derived as follows: c-vcos θ =L/t1 (Equation 1).

c+vcos θ=L/t2 (式2)。 c+vcos θ =L/t2 (Equation 2).

2vcos θ=L(1/t2-1/t1) (式3)。 2vcos θ = L(1/t2-1/t1) (Equation 3).

v=(t1-t2)/2cos θ*(L/(t1*t2)) (式4)。 v=(t1-t2)/2cos θ *(L/(t1*t2)) (Equation 4).

於上列方程式中,各參數代表的意義列示如下。c:聲速,L:量測路徑長度,θ:聲波傳送角度,v:流速,t1:逆流狀態下之聲波傳送時間,t2:順流狀態下之聲波傳送時間。 In the above equation, the meaning of each parameter is listed below. c: sound velocity, L: measurement path length, θ: sound wave transmission angle, v: flow velocity, t1: sound wave transmission time under countercurrent state, t2: sound wave transmission time under downstream state.

處理器131依據該些超平面方程式判斷量測到的流速組合所屬於的流場種類。接著處理器131依據已確認的流場種類從流量修正係數資料庫1321取得對應之流量修正係數。處理器131依據流量修正係數、流速組合與權重組合計算出流體的流量,而處理器131計算流體的流量之公式如下:Q=D*Vset*Wset (式5)。 The processor 131 determines the flow field type to which the measured flow velocity combination belongs according to the hyperplane equations. Then the processor 131 obtains the corresponding flow correction coefficient from the flow correction coefficient database 1321 according to the confirmed flow field type. The processor 131 calculates the flow rate of the fluid according to the flow correction coefficient, the flow rate combination and the weight combination, and the processor 131 calculates the flow rate of the fluid with the following formula: Q=D*Vset*Wset (Equation 5).

於上列式5中,各參數代表的意義列示如下。Q:流量,D:流量修正係數,Vset:流速組合,Wset:權重組合。 In the above formula 5, the meaning of each parameter is listed below. Q: flow, D: flow correction coefficient, Vset: flow rate combination, Wset: weight combination.

圖4係繪示本發明所揭露的管路流量量測系統應用於管路的第二實施態樣的示意圖。圖4與圖2之差異在於待測段T1為管路T的一部份,待測段T1介於管路T的入口端Ex以及出口端En之間,而第一感測器組11及第二感測器組12分別組接於待測段T1的相異二端。如此一來,第一感測器組11及第二感測器組12之間的量測路徑將不同於第一實施例的量測路徑。 4 is a schematic diagram showing a second embodiment of the pipeline flow measurement system disclosed in the present invention applied to pipelines. The difference between Fig. 4 and Fig. 2 is that the test section T1 is a part of the pipeline T, the test section T1 is between the inlet end Ex and the outlet end En of the pipeline T, and the first sensor group 11 and The second sensor group 12 is respectively grouped and connected to two different ends of the section T1 to be measured. As a result, the measurement path between the first sensor group 11 and the second sensor group 12 will be different from the measurement path of the first embodiment.

圖5係繪示本發明所揭露的管路流量量測系統應用於管路的第三實施態樣的示意圖。圖5與圖2之差異在於設置於管路T的入口端Ex的第一感測器的數量為一個。如此一來,傳遞於管路T的入口端Ex以及管路T的出口端En之間的感測訊號對為四筆,相對應地流速組合包含有四筆流速資料。 FIG. 5 is a schematic diagram showing a third embodiment of the pipeline flow measurement system disclosed in the present invention applied to pipelines. The difference between FIG. 5 and FIG. 2 is that the number of the first sensor provided at the inlet end Ex of the pipeline T is one. In this way, there are four pairs of sensing signals transmitted between the inlet end Ex of the pipeline T and the outlet end En of the pipeline T, and the corresponding flow velocity combination includes four flow velocity data.

在其他實施例中,設置於管路T的出口端En的第二感測器的數量為一個,而設置於管路T的入口端Ex的第一感測器的數量維持多 個。此外,管路T不限定為直管,亦可為曲管。 In other embodiments, the number of the second sensor provided at the outlet end En of the pipeline T is one, while the number of the first sensor provided at the inlet end Ex of the pipeline T remains large. A. In addition, the pipeline T is not limited to a straight pipe, and may be a curved pipe.

圖6係繪示本發明所揭露的量測管路流量的方法之第一實施例的方法流程圖,而前述管路流量量測系統的任一實施例均可執行圖6的方法。如圖6所示,在步驟S101,以控制器133分別致能組接於管路T的待測段的相異兩端的第一感測器組11以及第二感測器組12。在步驟S102,以處理器131讀取傳輸於第一感測器組11及第二感測器組12之間的多筆感測訊號對,其中感測訊號對的數量取決於第一感測器的數量以及第二感測器的數量。在步驟S103,以處理器131依據該些感測訊號對去計算出管路的待測段內的一流速組合,而該流速組合包含有多筆流速資料,其中流速資料的筆數等於感測訊號對的筆數。在步驟S104,以處理器131依據透過多次執行支持向量機而產生的多個不同的超平面方程式判斷管路的待測段內的流體的流速組合所屬於的流場種類。在步驟S105,以處理器131依據已確認的流體的流場種類,從流量修正係數資料庫1321取得對應該流場種類的流量修正係數。在步驟S106,以處理器131計算流速組合、權重組合以及流量修正係數之乘積以取得管路T的待測段內的流體的流量。 FIG. 6 is a method flowchart of the first embodiment of the method for measuring pipeline flow rate disclosed in the present invention, and any embodiment of the aforementioned pipeline flow rate measurement system can execute the method of FIG. 6. As shown in FIG. 6, in step S101, the controller 133 respectively enables the first sensor group 11 and the second sensor group 12 connected to different ends of the section to be measured of the pipeline T. In step S102, the processor 131 reads a plurality of sensing signal pairs transmitted between the first sensor group 11 and the second sensor group 12, wherein the number of the sensing signal pairs depends on the first sensor The number of sensors and the number of second sensors. In step S103, the processor 131 calculates a flow velocity combination in the pipeline to be measured according to the sensing signal pairs, and the flow velocity combination includes a plurality of flow velocity data, wherein the number of the flow velocity data is equal to the number of the sensing signals. The number of signal pairs. In step S104, the processor 131 determines the flow field type to which the combination of the flow velocity of the fluid in the test section of the pipeline belongs according to a plurality of different hyperplane equations generated by multiple executions of the support vector machine. In step S105, the processor 131 obtains the flow correction coefficient corresponding to the flow field type from the flow correction coefficient database 1321 according to the confirmed flow field type of the fluid. In step S106, the processor 131 calculates the product of the flow rate combination, the weight combination, and the flow correction coefficient to obtain the flow rate of the fluid in the section to be measured of the pipeline T.

在其他實施例中,可採用不同於支持向量機的監督式學習來產生多個分類演算法,而透過該些分類演算法來判斷管路的待測段內的流體的流速組合所屬於的流場種類。 In other embodiments, a supervised learning different from a support vector machine can be used to generate multiple classification algorithms, and the classification algorithms can be used to determine the flow rate combination of the fluid in the pipeline to be measured. Field type.

圖7係繪示圖6所揭露的判斷管路內的流體所屬於的流場種類的詳細流程圖,而圖8係繪示圖6所揭露的判斷管路內的流體所屬於的流場種類的示意圖。如圖7所示,在步驟S1041,舉例依據支持向量機的多項式核心函式(polynomial kernel function)將量測到的流速組合以投影至核心空間(kernel space),且該核心空間內包含有由該些超平面方程式所區分的多個區域空間,而該些區域空間分別對應不同的流場種類,其中該些超平面方程式所表示的多個超平面之間彼此互不交集。在步驟S1042,以處理器131判斷流速組合與該些超平面方程式之間的位置關係。在步驟 S1043,以該處理器131判斷流速組合所處的區域空間。 FIG. 7 is a detailed flowchart for determining the type of flow field of the fluid in the pipeline disclosed in FIG. 6, and FIG. 8 is a diagram showing the type of flow field of determining the fluid in the pipeline disclosed in FIG. 6 Schematic diagram. As shown in Figure 7, in step S1041, for example, according to the polynomial kernel function of the support vector machine, the measured flow velocity is combined to project the kernel space, and the core space includes The multiple regional spaces distinguished by the hyperplane equations correspond to different flow field types, and the hyperplanes represented by the hyperplane equations do not intersect each other. In step S1042, the processor 131 determines the positional relationship between the flow velocity combination and the hyperplane equations. In steps S1043: Use the processor 131 to determine the regional space where the flow rate combination is located.

如圖8所示,縱座標與橫座標的物理量可分別為流速組合(例如(V1,V2...V16))中之任二個流速(例如第一流速V1及第二流速V2)。在核心空間中包含有第一超平面HP1以及第二超平面HP2,第一超平面HP1所圍成的第一區域空間內分佈有同屬於第二流場f2的多個流體模型,第二超平面HP2所圍成的第二區域空間內分佈有同屬於第三流場f3的多個流體模型,而在第一區域空間之外以及第二區域空間之外分佈有屬於第一流場f1的多個流體模型。當處理器131判斷管路T內的流速組合位於第一區域空間內,則流體的流場種類屬於第二流場f2。 As shown in FIG. 8, the physical quantities of the ordinate and the abscissa can be any two flow rates (such as the first flow velocity V1 and the second flow velocity V2) in the flow velocity combination (such as (V1, V2...V16)). The core space contains a first hyperplane HP1 and a second hyperplane HP2. In the first area enclosed by the first hyperplane HP1, multiple fluid models belonging to the second flow field f2 are distributed. The second hyperplane HP1 Multiple fluid models belonging to the third flow field f3 are distributed in the second area space enclosed by the plane HP2, and multiple fluid models belonging to the first flow field f1 are distributed outside the first area space and outside the second area space. A fluid model. When the processor 131 determines that the flow velocity combination in the pipeline T is located in the first regional space, the flow field type of the fluid belongs to the second flow field f2.

圖9係繪示本發明建立流量修正係數的一實施例的方法流程圖。如圖9所示,在步驟S201:透過一流量計量測管路的待測段內的一流體模型的一實際流量。在步驟S202:以第一感測器組11以及第二感測器組12量測待測段內的多筆感測訊號對。在步驟S203:以處理器131依據該些感測訊號對去計算待測段內的一流速組合,該流速組合包含多個第一類型流速以及多個第二類型流速,其中第一類型流速的傳輸方向與通過管路的中心軸的截面相互垂直(意即水平流速),而權重組合包含多個第一類型權重以及多個第二類型權重,該些第一類型權重對應於該些第一類型流速,該些第二類型權重對應於該些第二類型流速。在步驟S204,以處理器131計算該些第一類型流速與該些第一類型權重之乘積以取得一估計流量。在步驟S205,以處理器131將估計流量除以實際流量以取得一流量修正係數。依據圖9的建立流量修正係數方法對其他多個不同的流體模型計算其實際流量以及估計流場,便可建立流量修正係數資料庫。 FIG. 9 is a flowchart of a method for establishing a flow correction coefficient according to an embodiment of the present invention. As shown in FIG. 9, in step S201: Measure an actual flow rate of a fluid model in the section to be measured in the pipeline through a flow meter. In step S202: use the first sensor group 11 and the second sensor group 12 to measure multiple pairs of sensing signals in the segment to be measured. In step S203: the processor 131 calculates a flow rate combination in the section to be measured according to the sensing signal pairs, the flow rate combination includes a plurality of first type flow rates and a plurality of second type flow rates, wherein the first type flow rate The transmission direction and the cross section passing through the central axis of the pipeline are perpendicular to each other (meaning horizontal flow velocity), and the weight combination includes multiple first-type weights and multiple second-type weights, and the first-type weights correspond to the first-type weights. Type flow rate, the second type weights correspond to the second type flow rates. In step S204, the processor 131 calculates the product of the first-type flow rates and the first-type weights to obtain an estimated flow rate. In step S205, the processor 131 divides the estimated flow rate by the actual flow rate to obtain a flow rate correction coefficient. According to the method of establishing flow correction coefficient in Fig. 9, calculate the actual flow and estimated flow field for other different fluid models, and then the flow correction coefficient database can be established.

由於非完全發展流的流速分佈不均,難以利用人工分類或一般線性迴歸方式對非完全發展流之流體進行準確地分類。因此在以運算裝置3讀取該些感測訊號對之前,執行一機器學習程序以建立流場種類分類資料庫1321,達到對非完全發展流之流體進行分類之目的。 Due to the uneven distribution of the flow velocity of the incompletely developed flow, it is difficult to use manual classification or general linear regression to accurately classify the incompletely developed flow. Therefore, before the arithmetic device 3 reads the sensing signal pairs, a machine learning program is executed to build the flow field classification database 1321, so as to achieve the purpose of classifying the fluids of the incompletely developed flow.

圖10係繪示執行機器學習程序建立流場種類分類資料庫的一實施例的流程圖。如圖10所示,機器學習以支持向量機為例,在步驟S301,收集多個不同流場種類的流體模型組合以作為一訓練樣本,其中每一流體模型組合包含多個不同的流體模型,而每一流體模型由多筆流速資料來表示。舉例來說,收集8個同屬於A流場的不同的流體模型以組成第一流體模型組合,以及收集10個屬於B流場的不同的流體模型以組成第二流體模組組合。在步驟S302,透過支持向量機分析該訓練樣本中屬於相同流場種類的流體模型的同質性。在步驟S303,依據同質性分析結果建立多個不同的超平面(hyper-plane)方程式,且該些超平面方程式形成多個區域空間,而該些區域空間分別對應不同的流場種類。 FIG. 10 is a flowchart of an embodiment of executing a machine learning program to build a flow field classification database. As shown in Fig. 10, machine learning takes a support vector machine as an example. In step S301, a plurality of fluid model combinations of different flow field types are collected as a training sample, wherein each fluid model combination includes a plurality of different fluid models. Each fluid model is represented by multiple flow velocity data. For example, 8 different fluid models belonging to the A flow field are collected to form the first fluid model combination, and 10 different fluid models belonging to the B flow field are collected to form the second fluid model combination. In step S302, the homogeneity of the fluid models belonging to the same flow field type in the training sample is analyzed through the support vector machine. In step S303, a plurality of different hyper-plane equations are established according to the homogeneity analysis result, and the hyper-plane equations form a plurality of regional spaces, and the regional spaces correspond to different flow field types.

Figure 108142158-A0305-02-0012-1
Figure 108142158-A0305-02-0012-1

表1的參數D為管路T的直徑,而管路T的總長為直徑的10倍,分別於管路T的2D、4D、6D、8D以及10D的截面處進行流場種類之判斷以及流量之計算,其中在2D~8D的位置流通的流體屬於非完全發展流。由表1可知,本發明所揭露的管路流量量測系統及量測管路流量的方法,有效地將流量誤差降低至2%以下,即便管路T的總長僅為直徑的2 倍,依據本發明所提供之量測管路流量的方法所計算出的流量能符合實際需求。 The parameter D in Table 1 is the diameter of the pipeline T, and the total length of the pipeline T is 10 times the diameter. The flow field type and flow rate are judged at the 2D, 4D, 6D, 8D, and 10D sections of the pipeline T. According to the calculation, the fluid circulating in the position of 2D~8D belongs to the incompletely developed flow. It can be seen from Table 1 that the pipeline flow measurement system and the method for measuring pipeline flow disclosed in the present invention effectively reduce the flow error to less than 2%, even if the total length of the pipeline T is only 2% of the diameter. The flow rate calculated according to the method for measuring pipeline flow rate provided by the present invention can meet actual requirements.

綜上所述,本發明所揭露的管路流量量測系統及量測管路流量的方法,例如具有透過多次執行支持向量機而建立的流場種類分類資料庫,解決了以往利用人工分類或一般線性迴歸方式無法對非完全發展流之流體進行分類的問題。如此一來,運算裝置便可依據流速資料精確判斷其所屬於的流場種類,依據流場種類找出對應的流量修正係數,依據流量修正係數計算出更精確的流體流量、依據精確的流量值可有效率地監控水側系統的效能,進而達到節能減碳的效果。 In summary, the pipeline flow measurement system and the method for measuring pipeline flow disclosed in the present invention have, for example, a classification database of flow field types established by multiple executions of support vector machines, which solves the problem of using manual classification in the past. Or the general linear regression method cannot classify the fluid of the incompletely developed flow. In this way, the computing device can accurately determine the type of flow field it belongs to based on the flow rate data, find the corresponding flow correction coefficient based on the flow field type, and calculate a more accurate fluid flow based on the flow correction coefficient, based on the accurate flow value The efficiency of the water side system can be monitored efficiently, and the effect of energy saving and carbon reduction can be achieved.

雖然本發明以前述之實施例揭露如上,然其並非用以限定本發明。在不脫離本發明之精神和範圍內,所為之更動與潤飾,均屬本發明之專利保護範圍。關於本發明所界定之保護範圍請參考所附之申請專利範圍。 Although the present invention is disclosed in the foregoing embodiments, it is not intended to limit the present invention. All changes and modifications made without departing from the spirit and scope of the present invention fall within the scope of the patent protection of the present invention. For the scope of protection defined by the present invention, please refer to the attached scope of patent application.

11第一感測器組 12第二感測器組 13運算裝置 131處理器 132記憶體 1321流場種類分類資料庫 1322流量修正係數資料庫 133控制器 134輸入操作介面 11 first sensor group 12 second sensor group 13 arithmetic device 131 processor 132 memory 1321 Flow Field Classification Database 1322 flow correction coefficient database 133 controller 134 input operation interface

Claims (13)

一種管路流量量測系統,用於量測一管路的一待測段內的流體的流量,該管路流量量測系統包括:一第一感測器組及一第二感測器組,該第一感測器組及該第二感測器組分別組接於該待測段的相異二端;以及一運算裝置,電性連接於該第一感測器組以及該第二感測器組,且依據傳輸於該第一感測器組及該第二感測器組之間的多筆感測訊號對,以計算一流速組合;其中該運算裝置儲存有透過多次執行一監督式學習而產生的多個分類演算法及一流量修正係數資料庫,該運算裝置依據該些分類演算法以判斷該流速組合所屬於的一流場種類,該運算裝置從該流量修正係數資料庫取得對應該流場種類的一流量修正係數,該運算裝置依據該流量修正係數以及該流速組合以計算該流量。 A pipeline flow measurement system for measuring the flow of fluid in a section to be measured of a pipeline. The pipeline flow measurement system includes: a first sensor group and a second sensor group , The first sensor group and the second sensor group are respectively connected to two different ends of the segment to be measured; and an arithmetic device is electrically connected to the first sensor group and the second sensor group A sensor group, and calculate a flow rate combination according to a plurality of sensor signal pairs transmitted between the first sensor group and the second sensor group; wherein the computing device stores a combination of multiple executions A plurality of classification algorithms and a flow correction coefficient database generated by a supervised learning. The calculation device determines the flow field type to which the flow velocity combination belongs based on the classification algorithms. The calculation device uses the flow correction coefficient data The library obtains a flow correction coefficient corresponding to the type of flow field, and the computing device calculates the flow according to the flow correction coefficient and the flow velocity combination. 如請求項1所述之管路流量量測系統,其中該監督式學習為一支持向量機,而該些分類演算法為多個不同的超平面方程式。 The pipeline flow measurement system according to claim 1, wherein the supervised learning is a support vector machine, and the classification algorithms are a plurality of different hyperplane equations. 如請求項1所述之管路流量量測系統,其中該運算裝置以該流量修正係數、該流速組合以及一權重組合之乘積以取得該流量。 The pipeline flow measurement system according to claim 1, wherein the calculation device obtains the flow rate by the product of the flow rate correction coefficient, the flow rate combination, and a weight combination. 如請求項1所述之管路流量量測系統,其中該第一感測器組包含多個第一感測器,該第二感測器組包含多個第二感測器,該待測段的該相異兩端分別為該管路的一入口端以及一出口端。 The pipeline flow measurement system according to claim 1, wherein the first sensor group includes a plurality of first sensors, the second sensor group includes a plurality of second sensors, and the to-be-tested The different ends of the segment are respectively an inlet end and an outlet end of the pipeline. 如請求項4所述之管路流量量測系統,其中該管路定義一中心軸以及一截面,且該中心軸位在該截面,該些第一感測器位於該截面的一側,而該些第二感測器位於該截面的另一側。 The pipeline flow measurement system according to claim 4, wherein the pipeline defines a central axis and a cross section, and the central axis is located on the cross section, the first sensors are located on one side of the cross section, and The second sensors are located on the other side of the cross section. 如請求項1所述之管路流量量測系統,其中該第一感測器組以及該第二感測器組組接於該管路的外部,該運算裝置通訊連接於該第一感測器組以及該第二感測器組。 The pipeline flow measurement system according to claim 1, wherein the first sensor group and the second sensor group are assembled outside the pipeline, and the computing device is communicatively connected to the first sensor Sensor group and the second sensor group. 如請求項1所述之管路流量量測系統,其中該運算裝置包含一處理器、一控制器以及一記憶體,該處理器電性連接該記憶體以及該控制器,該記憶體儲存該些分類演算法及該流量修正係數資料庫,該控制器電性連接於該第一感測器組以及該第二感測器組,該控制器用於接收一啟動指令以致能該第一感測器組以及該第二感測器組。 The pipeline flow measurement system according to claim 1, wherein the computing device includes a processor, a controller, and a memory, the processor is electrically connected to the memory and the controller, and the memory stores the The classification algorithms and the flow correction coefficient database, the controller is electrically connected to the first sensor group and the second sensor group, and the controller is used to receive a start command to enable the first sensor Sensor group and the second sensor group. 一種量測管路流量的方法,用於量測一管路的一待測段內的流體的流量,包括:以一運算裝置讀取傳輸於一第一感測器組及一第二感測器組之間的多筆感測訊號對;以該運算裝置依據該些感測訊號對計算該流體的一流速組合,其中該運算裝置儲存有透過多次執行一監督式學習而產生的多個分類演算法及一流量修正係數資料庫;以該些分類演算法判斷該流速組合所屬於的流場種類;以該流場種類從該流量修正係數資料庫取得對應該流場種類的一流量修正係數;以及以該運算裝置依據該流速組合以及該流量修正係數計算該流量。 A method for measuring pipeline flow rate, used to measure the flow rate of fluid in a section to be measured of a pipeline, including: reading and transmitting to a first sensor group and a second sensor with an arithmetic device A plurality of sensing signal pairs between the device group; the calculation device calculates a flow velocity combination of the fluid according to the sensing signal pairs, wherein the calculation device stores a plurality of generated by performing a supervised learning multiple times Classification algorithm and a flow correction coefficient database; use these classification algorithms to determine the flow field type to which the flow velocity combination belongs; use the flow field type to obtain a flow correction corresponding to the flow field type from the flow correction coefficient database Coefficient; and the calculation device calculates the flow rate according to the flow rate combination and the flow rate correction coefficient. 如請求項8所述之量測管路流量的方法,其中該監督式學習為一支持向量機,而該些分類演算法為多個不同的超平面方程式。 The method for measuring pipeline flow according to claim 8, wherein the supervised learning is a support vector machine, and the classification algorithms are a plurality of different hyperplane equations. 如請求項8所述之量測管路流量的方法,其中該運算裝置以該流速組合、該流量修正係數以及一權重組合之乘積以取得該流量。 The method for measuring pipeline flow according to claim 8, wherein the computing device obtains the flow by the product of the flow velocity combination, the flow correction coefficient, and a weight combination. 如請求項8所述之量測管路流量的方法,更包含在以該運算裝置讀取該些感測訊號對之前,執行一機器學習程序,該機器學習程序包含:收集不同流場種類的多個流體模組組合以作為一訓練樣本,而每一流體模型組合包含多個不同的流體模型;以及透過對於該訓練樣本執行多次該監督式學習以產生該些分類演算法。 The method for measuring pipeline flow as described in claim 8, further comprising executing a machine learning program before reading the sensing signal pairs by the computing device, the machine learning program including: collecting data of different flow field types A plurality of fluid module combinations are used as a training sample, and each fluid model combination includes a plurality of different fluid models; and the supervised learning is performed multiple times on the training sample to generate the classification algorithms. 如請求項8所述之量測管路流量的方法,其中該第一感測器組包含多個第一感測器,該第二感測器組包含多個第二感測器,每一第一感測器發出一第一感測訊號由該些第二感測器所接收,每一第二感測器發出一第二感測訊號由該些第一感測器所接收。 The method for measuring pipeline flow according to claim 8, wherein the first sensor group includes a plurality of first sensors, and the second sensor group includes a plurality of second sensors, each The first sensor emits a first sensing signal that is received by the second sensors, and each second sensor emits a second sensing signal that is received by the first sensors. 如請求項12所述之量測管路流量的方法,其中該管路定義一中心軸以及通過該中心軸的一截面,且該中心軸位在該截面,該些第一感測器與該些第二感測器之間包含有多個不同的量測路徑,該些量測路徑的一部份通過該中心軸。 The method for measuring pipeline flow according to claim 12, wherein the pipeline defines a central axis and a section passing through the central axis, and the central axis is located on the section, the first sensors and the A plurality of different measurement paths are included among the second sensors, and a part of the measurement paths passes through the central axis.
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