Crack growth prediction system and crack growth prediction method

Abstract

To provide a crack development prediction system and a crack development prediction method capable of highly accurately estimating the behavior of crack development from actual measurement data of the depth of a crack obtained by a plurality of times of nondestructive inspection.SOLUTION: A control device of a crack progress prediction system acquires actual measurement data in which a measurement value of a depth of a crack obtained by a non-destructive inspection is associated with a measurement time point, performs a crack progress analysis for each of a plurality of analysis conditions to calculate an analysis value of the depth of the crack at each of a plurality of time points for each of the plurality of analysis conditions, calculates a difference between the analysis value and the measurement value of the depth of the crack for each of the plurality of time points, and calculates a probability density on the basis of the calculated difference and reference data of a probability density distribution of a measurement error by a predetermined non-destructive inspection. The probability density distribution of the depth of the crack is updated based on the probability density calculated for each of the plurality of time points, the crack progress evaluation is performed based on the updated probability density distribution of the depth of the crack, and the result of the crack progress evaluation is output.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a crack growth prediction system and a crack growth prediction method. [Background technology]

[0002] In power plants where the ageing of plants is progressing, improving the accuracy of health assessment techniques for aging equipment is important for improving safety and extending the lifespan of the plant. For example, if a crack is found during non-destructive testing of the piping of a nuclear power plant, an assessment is made using fracture mechanics to determine whether operation is possible until the next regular inspection. Remaining life assessments using non-destructive testing and fracture mechanics are based on assessment methods that fully ensure the safety of nuclear power plants. On the other hand, from the perspective of the economics of operating nuclear power plants, it is necessary to proceed with rationalization while ensuring sufficient safety.

[0003] Patent Document 1 proposes a crack growth prediction technology that aims to predict the growth of cracks in a structure without being overly conservative in its evaluation. In the crack growth prediction technology described in Patent Document 1, an analytical variance is set for the crack growth predicted by finite element analysis based on the probabilistic variance obtained by probabilistic prediction, and the growth of the crack over the service life is predicted based on the crack growth for which the analytical variance has been set. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2020-186967 Summary of the Invention [Problem to be solved by the invention]

[0005] However, the technology described in Patent Document 1 predicts crack growth based on initial measurement results, and does not provide feedback on the dimensions of the crack as it grows over time. Therefore, there is room for improvement in terms of the accuracy of estimating crack growth behavior.

[0006] The present invention aims to provide a crack propagation prediction system and a crack propagation prediction method that can estimate crack propagation behavior with high accuracy from actual crack depth measurement data obtained by multiple non-destructive inspections. [Means for solving the problem]

[0007] A crack propagation prediction system according to one aspect of the present invention includes a control device that performs a crack propagation evaluation of an equipment to be evaluated. The control device acquires actual measurement data that corresponds the measurement value of the crack depth obtained by non-destructive testing with the time point at which the measurement was made, performs a crack propagation analysis for each of a plurality of analysis conditions in which at least one of a plurality of parameters including the initial value of the crack depth and the crack propagation rate is different, calculates an analysis value of the crack depth for each of the plurality of time points for each of the analysis conditions, calculates the difference between the analysis value and the measurement value of the crack depth for each of the plurality of time points, calculates a probability density based on the calculated difference and predetermined reference data for a probability density distribution of measurement error by non-destructive testing, updates the probability density distribution of the crack depth based on the probability density calculated for each of the plurality of time points, performs a crack propagation evaluation based on the updated probability density distribution of the crack depth, and outputs the results of the crack propagation evaluation. A crack propagation prediction method according to one aspect of the present invention includes the steps of: acquiring actual measurement data corresponding to the measurement values ​​of crack depth obtained by non-destructive testing performed on the equipment to be evaluated and the time points at which the measurements were made; performing a crack propagation analysis for each of a plurality of analysis conditions in which at least one of a plurality of parameters including the initial value of the crack depth and the crack propagation rate is different, and calculating an analysis value of the crack depth for each of the plurality of time points for each of the analysis conditions; calculating the difference between the analysis value and the measurement value of the crack depth for each of the plurality of time points; calculating a probability density based on the calculated difference and predetermined reference data for a probability density distribution of measurement error by non-destructive testing; updating the probability density distribution of the crack depth based on the probability density calculated for each of the plurality of time points; performing a crack propagation evaluation based on the updated probability density distribution of the crack depth; and outputting the results of the crack propagation evaluation. [Effects of the Invention]

[0008] According to the present invention, it is possible to provide a crack propagation prediction system and a crack propagation prediction method that can estimate crack propagation behavior with high accuracy from actual crack depth measurement data obtained by multiple non-destructive inspections. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a functional block diagram of a crack growth prediction system according to this embodiment. [Figure 2] FIG. 2 is a flowchart showing an example of the flow of processing executed by the control device. [Figure 3] FIG. 3 shows the results of the crack propagation analysis. [Figure 4] FIG. 4 is a diagram showing the difference dai between the crack depth analysis value ai Cal and the crack depth measurement value ai Insp, and the probability density distribution of the measurement error set with the crack depth analysis value ai Cal as the median. [Figure 5]FIG. 5 is a diagram showing the sum pn of the probability density and a probability density distribution Di newly calculated using the sum pn of the probability density. [Figure 6] FIG. 6 shows the results of evaluating the crack propagation behavior using the updated probability density function. [Figure 7] FIG. 7 is a diagram illustrating an example of a conventional crack growth evaluation method. DETAILED DESCRIPTION OF THE INVENTION

[0010] FIG. 1 is a functional block diagram of a crack propagation prediction system 1 according to this embodiment. As shown in FIG. 1, the crack propagation prediction system 1 includes an inspection device 4 that performs non-destructive testing of the equipment to be evaluated, a display device 2 such as a liquid crystal monitor, and a control device 100 that performs a crack propagation evaluation of the equipment to be evaluated using the inspection results of the inspection device 4 and controls the display device 2 to display the evaluation results on the display screen of the display device 2. Various information (data) such as operating history information of the equipment to be evaluated is input to the control device 100 from an external device 5. The equipment to be evaluated is, for example, a nuclear reactor, a heat exchanger, piping, or other equipment installed in a nuclear power plant. The external device 5 is, for example, an external server, an external storage device, an input device, or the like. The input device is, for example, a keyboard, a switch box, or the like that can be operated by an administrator.

[0011] The inspection device 4 is connected to the control device 100 and performs non-destructive testing of the evaluation target equipment at any timing, not only when the evaluation target equipment is stopped but also when the evaluation target equipment is operating, and outputs the inspection results to the control device 100. The control device 100 acquires the inspection results of the inspection device 4 not only when the evaluation target equipment is stopped but also when the evaluation target equipment is operating. The control device 100 evaluates the crack growth of the evaluation target equipment each time it acquires an inspection result. In this manner, the crack growth prediction system 1 according to this embodiment uses a permanently installed inspection device 4 to constantly monitor cracks during operation of the evaluation target equipment. Note that crack growth refers to the expansion of crack dimensions over time. In this embodiment, the latest inspection results from the inspection device 4 are fed back to perform crack growth evaluation. Therefore, according to this embodiment, the behavior of crack growth can be estimated with high accuracy.

[0012] <Control device hardware configuration> The control device 100 is composed of a computer equipped with processing devices such as a CPU (Central Processing Unit), MPU (Micro Processing Unit), and DSP (Digital Signal Processor), non-volatile memory such as ROM (Read Only Memory), flash memory, and hard disk drive, volatile memory known as RAM (Random Access Memory), an input / output interface, and other peripheral circuits. These hardware components work together to run software and realize multiple functions. The controller may be composed of one computer or multiple computers. The processing device may be an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or the like.

[0013] The nonvolatile memory stores programs capable of executing various calculations. In other words, the nonvolatile memory is a storage medium (storage device) from which the programs that realize the functions of this embodiment can be read. The volatile memory is a storage medium (storage device) that temporarily stores the results of calculations performed by the processing device and signals input from the input / output interface. The processing device is a device that loads the programs stored in the nonvolatile memory into the volatile memory and executes calculations, and performs predetermined calculations on data taken from the input / output interface, the nonvolatile memory, and the volatile memory in accordance with the programs.

[0014] The input section of the input / output interface converts a signal input from the external device 5 into data that can be calculated by the processing device. The output section of the input / output interface generates an output signal according to the calculation result in the processing device, and outputs the signal to the display device 2.

[0015] <Conventional crack growth evaluation method> An example of a conventional crack propagation evaluation method will be described with reference to FIG. 7. In FIG. 7, the horizontal axis represents time, and the vertical axis represents the depth of the crack in the equipment being evaluated. As shown in FIG. 7, in the conventional crack propagation evaluation method, a remaining life evaluation is performed based on fracture mechanics using the depth of the crack measured by non-destructive testing during a periodic inspection (hereinafter also referred to as crack depth) as a reference. Here, it is recommended that non-destructive testing be performed about three times at the maximum echo position, and multiple measurements are performed. The example shown in FIG. 7 shows an example in which three measurements were performed during each periodic inspection, and the measured values ​​of the crack depth are indicated by open circles.

[0016] The crack depth used in the evaluation is the maximum value of multiple measurements. As a result, the measured crack depth is often estimated to be larger than the actual crack due to measurement errors in non-destructive testing. This can lead to the crack depth being determined to exceed the limit depth (allowable value) before the next periodic inspection, resulting in the need to replace the part. Furthermore, fatigue crack growth evaluation uses conservative values ​​for material parameters such as the acting stress and crack growth rate, resulting in evaluation results that are overly likely to be true. Furthermore, conventional crack growth evaluation methods do not accurately capture the variance in measurement values ​​or remaining life assessment techniques, making it impossible to quantitatively evaluate the remaining life of actual equipment.

[0017] <Crack Growth Evaluation Method of the Present Embodiment> In this embodiment, a crack propagation prediction system 1 and a crack propagation prediction method are provided that can improve the accuracy of crack propagation evaluation using the results of crack propagation analysis and non-destructive testing. The control device 100 executes a program stored in a storage device, thereby executing each step of the crack propagation prediction method. Below, the functions of the control device 100 of the crack propagation prediction system 1 according to this embodiment and the details of the processes executed will be described.

[0018] <Controller function> As shown in Figure 1, the control device 100 has functions as an operating history recording unit 101, a crack propagation analysis unit 102, a non-destructive testing unit 103, a crack dimension error evaluation unit 104, a crack propagation evaluation unit 105, and a result output unit 106.

[0019] <Driving history recording section> The operation history recording unit 101 acquires and stores operation history information of the equipment to be evaluated from the external device 5. The operation history information is used to determine boundary conditions such as stress used in crack propagation analysis. The operation history information includes, for example, time history data of the operating state and time history data of various measurement values. The time history data of the operating state is historical data of the time when the operating state changed, such as the start time, stop time, and time when the output changed of the equipment to be evaluated. The time history data of various measurement values ​​is historical data that associates measurement values ​​such as temperature, pressure, strain at a specified location, and water quality of a fluid passing through a specified location with the time of measurement. The specified location is, for example, a measurement location for non-destructive testing in the equipment to be evaluated and its surrounding area.

[0020] <Crack Growth Analysis Section> The crack propagation analysis unit 102 sets the conditions necessary for the crack propagation analysis based on the operation history information stored in the operation history recording unit 101, and performs the crack propagation analysis based on the set conditions. The crack propagation analysis unit 102 performs the crack propagation analysis based on the calculation result of the stress intensity factor using the simple evaluation formula.

[0021] The crack growth analysis unit 102 will be described in detail below. The crack growth analysis unit 102 includes a basic condition setting unit 121, a random number generation unit 122, an evaluation database 123, an analysis condition setting unit 124, and a crack growth calculation unit 125.

[0022] The basic condition setting unit 121 sets basic conditions for analysis according to the part of the equipment to be evaluated (hereinafter also referred to as the evaluation part) to be evaluated, the expected operating conditions (operation history information), etc. The basic conditions include the shape and dimensions of the part to be evaluated, as well as stress conditions (load conditions). For example, if start-up and shutdown are assumed, the basic conditions include distribution data such as the stress range of the part to be evaluated that occurs in one repeated cycle, and temperature distribution. The basic conditions also include the number of cases N for which the crack growth analysis unit 102 calculates the crack growth analysis. The number of cases N corresponds to the number of analysis conditions, which will be described later. The number of cases N is set to an arbitrary value by an external device (input device) 5.

[0023] The random number generator 122 generates random numbers for each parameter in order to perform a probabilistic evaluation of the cumulative probability distribution of the stress and material properties (strength, elastic-plastic properties, crack growth rate, etc.) used in the evaluation. The random number generator 122 generates random numbers with values ​​in the range of 0 to 1.

[0024] The evaluation database 123 stores in advance data related to the variability of each parameter used in the evaluation (stress, inspection accuracy, material properties). The evaluation database 123 includes initial value data such as initial crack dimensions. The evaluation database 123 also includes a crack growth characteristic database and a stress analysis database. The crack growth characteristic database stores data on crack growth characteristics used in crack growth analysis, such as crack growth rate. The stress analysis database stores data on stress analysis results for each operating state. The range and variability information of each parameter is expressed as a continuous probability function using a probability distribution (normal distribution, Weibull distribution, etc.) suited to each characteristic.

[0025] The analysis condition setting unit 124 determines the value of each parameter used in the crack growth analysis by using a random number (0 to 1) generated by the random number generating unit 122 and matching it with the probability density distribution of each parameter stored in the evaluation database 123. The analysis condition setting unit 124 sets N cases of analysis conditions in which at least one of a plurality of parameters including the initial crack depth (initial value of the crack depth) and the crack growth rate is different.

[0026] The crack growth calculation unit 125 performs crack growth analysis by deterministic calculation based on each parameter (fixed value) such as the initial crack depth and crack growth rate that constitute the analysis conditions determined by the analysis condition setting unit 124. The crack growth calculation unit 125 performs crack growth analysis based on determinism for each of a plurality of analysis conditions. As a result, analytical values ​​of the crack depth at each of a plurality of time points are obtained for each of a plurality of analysis conditions.

[0027] As described above, the crack propagation analysis unit 102 generates a random number within a predetermined range and sets each parameter within the predetermined range by multiplying the random number by the reference value (median) of the parameter. In other words, the crack propagation analysis unit 102 sets N cases of analysis conditions. The crack propagation analysis unit 102 performs crack propagation analysis based on each parameter for all N cases of analysis conditions. In other words, the crack propagation analysis is repeatedly performed until the number of analyses reaches N.

[0028] <Non-Destructive Inspection Department> The non-destructive testing unit 103 acquires the test results from the testing device 4, measures crack dimensions based on the test results, and stores the measurement results. The testing device 4 is a non-destructive testing device capable of performing common non-destructive testing methods such as ultrasonic testing, eddy current testing, and potential difference testing. The measurement errors for each measurement method are evaluated and stored in advance. In this embodiment, the permanent testing device 4 continuously measures crack dimensions by non-destructive testing during operation.

[0029] The non-destructive inspection unit 103 will be described in detail below. The non-destructive inspection unit 103 includes a crack measurement unit 131, a measurement result database 132, and a non-destructive inspection accuracy database 133.

[0030] The crack measurement unit 131 acquires the inspection results of the non-destructive inspection performed using the inspection device 4, and measures the crack dimensions of the evaluation portion of the equipment to be evaluated based on the acquired inspection results. The crack dimensions include information on the depth, size (crack surface length), and shape of the crack (defect). Various calculations for crack depth will be explained below as a representative example.

[0031] The crack measurement unit 131 acquires the measurement value of the crack depth by calculating the measurement value of the crack depth based on the inspection results of the inspection device 4 while the evaluation target equipment is stopped and while it is in operation. In addition, the time when the measurement value is calculated (i.e., the time when the crack depth is measured) is stored in the measurement result database 132 in association with the measurement value, which is the calculation result.

[0032] The measurement result database 132 stores time history data of crack dimensions measured by non-destructive testing of a predetermined evaluation location (same part). The time history data is historical data of actual measurement data in which the measurement values ​​of crack depths obtained by non-destructive testing are associated with the time points at which the measurements were made. The inspection device 4 repeatedly performs inspections at predetermined intervals and outputs the inspection results to the control device 100. Therefore, new actual measurement data is added to the measurement result database 132 every time a predetermined period has elapsed. The predetermined period is shorter than the interval between regular inspections.

[0033] The nondestructive testing accuracy database 133 is a database related to measurement errors (measurement dimensional accuracy) of crack depths (defects) in the applied nondestructive testing method. The nondestructive testing accuracy database 133 stores reference data for the probability density distribution of crack depth measurement errors in advance. The reference data for the probability density distribution of crack depth measurement errors is modeled using a continuous probability distribution. In this embodiment, the probability density distribution of the measurement errors is expressed as a continuous probability function using a normal distribution. Note that the probability density distribution may be a probability density distribution that matches the actual measurement errors, and may be modeled using a Weibull distribution, a log-normal distribution, or the like.

[0034] <Crack Dimension Error Evaluation Section> The crack dimension error evaluation unit 104 compares the results of the crack propagation analysis performed for each of multiple analysis conditions with the results of the non-destructive testing, probabilistically evaluates the evaluation error of the crack depth at the time of measurement based on the measurement error of the non-destructive testing, and updates the prediction error of the crack depth.

[0035] A detailed description will be given of the crack dimension error evaluation unit 104. The crack dimension error evaluation unit 104 includes a dimension error evaluation unit 141 and an error update unit 142.

[0036] The dimensional error evaluation unit 141 i The dimensional error evaluation unit 141 compares the measured crack depth of the evaluation portion with the analytical crack depth at each time point t i The error (hereinafter simply referred to as the difference) between the analytical value (predicted value) and the measured value is calculated.

[0037] That is, the dimension error evaluation unit 141 performs the dimension error evaluation at multiple points in time t i For each crack depth, the analytical value a i Cal and the measured value a i Insp The difference between i Specifically, the dimensional error evaluation unit 141 calculates the analytical value a of the crack depth calculated for each of the plurality of analysis conditions. i Cal The measured crack depth a obtained by non-destructive testing is the median value. i Insp The difference between i Here, at time t i The time t is the time when the measurement value of the crack depth is calculated by the inspection device 4 and the non-destructive inspection unit 103, that is, the time when the crack depth is measured. i The analytical value is calculated at t. i is an integer between 0 and n, and increases by one each time the number of measurements (number of inspections) increases. n corresponds to the time when the latest measurement value was obtained.

[0038] The dimensional error evaluation unit 141 i Error da i Specifically, the dimensional error evaluation unit 141 calculates the probability density of the sizing accuracy (inspection accuracy) from the calculated difference da i and reference data of the probability density distribution of measurement errors by non-destructive testing that is predetermined. The reference data of the probability density distribution is stored in the non-destructive testing accuracy database 133, as described above.

[0039] Furthermore, the dimension error evaluation unit 141 evaluates the dimension error at a predetermined time point (in this embodiment, the time point t n ) until time t i The sum of the probability densities calculated for each i is calculated for each of a plurality of analysis conditions.

[0040] The error update unit 142 updates the crack propagation analysis result obtained by the dimensional error evaluation unit 141 at time t nThe sum of the probability densities up to p n The probability density distribution of the crack depth is updated based on the analysis results (analysis results for N cases) for all the analysis conditions calculated. i Crack depth a in each crack growth analysis result i and all the time points t1 to t n The sum of the probability densities in p n From the relationship between each time point t1~t n The probability density distribution of the crack depth at

[0041] The error update unit 142 calculates the sum of the probability densities p n Based on the analytical value of the crack depth and the crack depth, at a predetermined time t n Update the median, standard deviation and variance of the predicted crack depth at

[0042] <Crack Growth Evaluation Section> If the crack growth evaluation unit 105 determines that the number of evaluations (N) in the crack growth analysis by the crack growth analysis unit 102 is sufficient, it performs a crack growth evaluation using the analysis results of the crack growth analysis unit 102 and the probability density distribution of the updated crack depth. If the crack growth evaluation unit 105 determines that the number of evaluations in the crack growth analysis unit 102 is insufficient, it performs an additional crack growth analysis and then performs a crack growth evaluation using the crack growth analysis results and the probability density distribution of the updated crack depth. The crack growth evaluation by the crack growth evaluation unit 105 is performed based on probabilistic fracture mechanics (PFM).

[0043] <Result output section> The result output unit 106 outputs the results of the crack growth evaluation to the display device 2. The display device 2 outputs an image showing the results of the crack growth evaluation to the display screen.

[0044] 2 is a flowchart showing an example of the flow of processing executed by the control device 100. The processing shown in the flowchart in FIG. 2 is started when an evaluation execution condition is met. The evaluation execution condition is met, for example, when the inspection result of the crack depth is input from the inspection device 4, that is, when a non-destructive inspection is performed. Note that the evaluation execution condition may be the input of the inspection result of one non-destructive inspection, or the input of the inspection results of multiple non-destructive inspections.

[0045] 2, in step S105, the control device 100 acquires and stores information about the results of the non-destructive inspection. i and the measured crack depth a i Insp and is input to the control device 100 by the external device 5. Methods of inputting the results of the non-destructive testing to the control device 100 include, for example, inputting using an input device such as a keyboard, inputting from an external server via a communication device, and inputting using an external storage device (storage medium).

[0046] In the next step S110, the control device 100 performs a crack propagation analysis under a plurality of analysis conditions using parameters such as the initial crack size and crack propagation rate. The analysis conditions are set based on the operating conditions. The crack propagation analysis is performed using the Monte Carlo method. As described above, the initial value data such as the initial crack size used in the crack propagation analysis, and the crack propagation rate characteristics are stored in the evaluation database 123. The control device 100 generates random numbers by the inverse function method using the probability distribution of parameters such as the initial crack size and crack propagation rate, and sets each parameter within the range expected under the operating conditions. The number of analysis trials (number of studies) N here is set to 10 from the perspective of performing probabilistic processing. 4 It is recommended to set it to 10 times or more. 4 The above analysis conditions are set, and a crack propagation analysis is carried out under each analysis condition.

[0047] In the next step S115, the control device 100 calculates the crack propagation time t i Analytical value of crack depth at a i Cal is extracted and stored.

[0048] Figure 3 shows the results of the crack propagation analysis. In Figure 3, the horizontal axis represents time t, and the vertical axis represents the crack depth a. In Figure 3, the results of the non-destructive testing performed at an arbitrary timing, i.e., the measured value of the crack depth a i Insp In Figure 3, 10 4 The results (crack propagation analysis results) calculated after more than 100 analysis trials are shown by the dashed-dotted lines. In Figure 3, the actual propagation behavior is shown by the solid line.

[0049] As shown in FIG. 2, in the next step S120, the control device 100 calculates the analysis value a of the crack depth obtained by the crack propagation analysis. i Cal and the measured crack depth a obtained by non-destructive testing i Insp The difference between i At time t i The control device 100 calculates the analytical value a of the crack depth. i Cal is used as a reference value (median) to set reference data for the probability density distribution of measurement errors in non-destructive testing. The control device 100 calculates the probability density f(da i ) is calculated. i and probability density f(da i ) is calculated for each case. As described above, the reference data of the probability density distribution of the measurement error in the non-destructive inspection is stored in advance in a storage device as, for example, normally distributed data.

[0050] Figure 4 shows the analytical value of the crack depth a i Cal and the measured crack depth a i Insp The difference between i and analytical value of crack depth ai Cal 4 is a diagram showing the probability density distribution of the measurement error, where the median value is set to . In FIG. 4, the horizontal axis represents time t, and the vertical axis represents the crack depth a. In FIG. 4, the analytical value a of the crack depth in a given case (given analytical conditions) is i Cal is shown by the dashed line. In Fig. 4, the measured crack depth a i Insp In Fig. 4, the analytical value of the crack depth a i Cal The probability density distribution (reference data) of the measurement error, which is set as the median, is shown by a solid line. As shown in FIG. 4, the control device 100 calculates the difference da at each time point t0, t1, t2, and t3 in a given case. i and the probability density f(da i ) for each of the N cases. i and probability density f(da i ) is calculated.

[0051] As shown in FIG. 2, in the next step S125, the control device 100 i (i=0~n) corresponding to the difference da i The probability density f(da i ) multiplied by p n Calculate the sum of the probability densities p n is expressed by the following equation (1).

[0052]

number

[0053] In the next step S130, the control device 100 i At each measurement point i, the analytical value of the crack depth a calculated for all cases is i Cal Based on the analytical value of the crack depth a i Cal The result of this calculation is the predicted crack depth a i PreFurthermore, the control device 100 determines the median value of the time t i (For each measurement point i), the sum of the probability densities calculated for all cases, p n and analytical value of crack depth a i Cal Based on the analytical value of the crack depth a i Cal The standard deviation and variance of the predicted crack depth a are calculated. i Pre It is also written as the standard deviation and variance of.

[0054] Figure 5 shows the sum of the probability densities p n and the sum of the probability densities p n The newly calculated probability density distribution D i 5 is a diagram showing the crack depth a and the probability density f. In FIG. 5, the horizontal axis represents the crack depth a, and the vertical axis represents the probability density f. In FIG. 5, the total multiplier p1 at i=1 is indicated by a hollow circle. Based on the total multiplier p1 calculated for each case (each analysis condition), a probability density distribution D1 of the crack depth after i=1 is calculated. When non-destructive testing is performed once, the result of the non-destructive testing at t1 is obtained. Therefore, the total multiplier p1 and the probability density distribution D1 at i=1 are obtained. In FIG. 5, the total multiplier p3 at i=3 is indicated by a black circle. Based on the total multiplier p3 calculated for each case (each analysis condition), a probability density distribution D3 of the crack depth after i=3 is calculated. When non-destructive testing is performed three times, the results of the non-destructive testing at t1, t2, and t3 are obtained. Therefore, the total multiplier p3 and the probability density distribution D3 at i=3 are obtained.

[0055] Probability density distribution D i is obtained by approximating the sum of the probability densities of all cases, pi, that is, the product of the probability densities, with a normal distribution. i is calculated as an approximate function and stored in a storage device. The predicted value a1 of the crack depth for i=1 shown in FIG. Pre The median of the analysis value a1 for all cases at i=1 Cal The probability density distribution D1 is calculated using the calculated result as the median. Similarly, the predicted value a3 of the crack depth for i=3 shown in FIG. PreThe median value of is the analysis value a3 of all cases at i=3. Cal The probability density distribution D3 is calculated using this calculation result as the median. As shown in Figure 5, the variation in crack depth decreases as the number of non-destructive inspections increases (as i increases).

[0056] As mentioned above, for each measurement point i (time t i By evaluating the value of the standard deviation (standard deviation in this case) and median of the crack size at each measurement point i after updating, the predicted values ​​are obtained.

[0057] 2, in the next step S135, the control device 100 evaluates the crack propagation behavior using the updated conditions, i.e., the new probability density distribution (probability density function). n Based on the probability density distribution of the predicted crack depth at the time, a process is performed to probabilistically predict the size of the crack as it grows over time.

[0058] Figure 6 shows the results of evaluating crack propagation behavior using the updated probability density function. As shown in Figure 6, the more nondestructive testing is performed, the smaller the variance in crack depth becomes, making it possible to evaluate crack propagation behavior probabilistically with higher accuracy than conventional methods. Furthermore, for crack propagation after the last measurement point, it is possible to evaluate crack propagation based on probabilistic fracture mechanics using the probability distribution of crack propagation behavior before that, making it possible to evaluate crack propagation behavior with higher accuracy than conventional methods.

[0059] As shown in FIG. 2, in the next step S140, the control device 100 calculates and updates the remaining life of the equipment to be evaluated based on the analysis results based on probabilistic fracture mechanics. In the next step S145, the control device 100 compares the remaining life updated in step S140 with a threshold value to determine whether or not replacement of the part including the evaluation portion is necessary. If the remaining life is longer than the threshold value, it determines that part replacement is not necessary, and the process shown in the flowchart of FIG. 2 ends. If the remaining life is equal to or shorter than the threshold value, it determines that part replacement is necessary, and the process proceeds to step S150. In step S150, the control device 100 outputs an image to the display device 2 prompting the administrator to perform replacement, and the process shown in the flowchart of FIG. 2 ends.

[0060] When the control device 100 acquires a measurement value at a new time point, it again executes the series of processes shown in the flowchart of Fig. 2. In other words, every time the control device 100 acquires a new measurement value, it updates the probability density distribution of the crack depth and performs a crack growth evaluation based on probabilistic fracture mechanics.

[0061] As described above, the crack propagation prediction method according to this embodiment uses the measured crack depth a obtained by the non-destructive inspection performed on the equipment to be evaluated. i Insp and the measured time t i and a step (S105) of acquiring actual measurement data in which the initial value of the crack depth and the crack growth rate are associated with each other, and performing a crack growth analysis for each of a plurality of analysis conditions in which at least one of a plurality of parameters including the initial value of the crack depth and the crack growth rate is different, and acquiring actual measurement data for each of a plurality of analysis conditions (for each N cases) at a plurality of time points t i Analytical value of crack depth a i Cal and steps (S110, S115) of calculating the time t i For each crack, the analytical value of the crack depth a i Cal and the measured value a i Insp The difference between i A step (S120) of calculating the difference da iBased on the predetermined reference data of the probability density distribution of the measurement error by non-destructive testing, the probability density f(da i ) at a plurality of time points t i The probability density f(da i ), the steps of performing a crack propagation evaluation based on the updated probability density distribution of the crack depth (S135, S140, S145), and the step of outputting the results of the crack propagation evaluation (S150).

[0062] According to the above-described embodiment, the following advantageous effects are achieved.

[0063] (1) The crack propagation prediction system 1 includes a control device 100 that performs crack propagation evaluation of the equipment to be evaluated. The control device 100 receives a measured value a of the depth of the crack obtained by non-destructive testing. i Insp and the measured time t i The control device 100 performs a crack growth analysis for each of a plurality of analysis conditions in which at least one of a plurality of parameters including the initial value of the crack depth and the crack growth rate is different, and acquires actual measurement data corresponding to the initial value of the crack depth and the crack growth rate. i Analytical value of crack depth a i Cal The control device 100 calculates the i For each crack, the analytical value of the crack depth a i Cal and the measured value a i Insp The difference between i The control device 100 calculates the calculated difference da i Based on the predetermined reference data of the probability density distribution of the measurement error by non-destructive testing, the probability density f(da i The control device 100 calculates the time t i The probability density distribution of the crack depth is updated based on the probability density calculated for each test, and a crack growth evaluation is performed based on the updated probability density distribution, and the results of the crack growth evaluation are output.

[0064] This configuration allows for highly accurate estimation of crack propagation behavior from actual crack depth measurement data (historical data) obtained through multiple non-destructive inspections, thereby reducing the frequency of part replacement and maintenance costs.

[0065] (2) The crack propagation prediction system 1 includes an inspection device 4 that performs non-destructive inspection of the evaluation target equipment while the evaluation target equipment is in operation. The control device 100 calculates a measured value a of the depth of the crack based on the inspection result of the inspection device 4 while the evaluation target equipment is in operation. i Insp The crack depth measurement value a i Insp The control device 100 acquires the new measured value a i Insp The probability density distribution of the crack depth is updated each time a measurement is acquired. With this configuration, the probability density distribution is updated each time the number of measurements (measurement points) increases, improving the accuracy of crack propagation predictions.

[0066] (3) The control device 100 calculates the analysis value a of the crack depth calculated for each of the plurality of analysis conditions. i Cal The measured crack depth a obtained by non-destructive testing is the median value. i Insp The difference between i The control device 100 calculates the calculated difference da i Based on the reference data of the probability density distribution of the measurement error, the probability density f(da i ) at a predetermined time t n Time t until i The sum of the probability densities calculated for each n The control device 100 calculates the sum of the probability densities p calculated for each of the plurality of analysis conditions. n and analytical value of crack depth a i Cal Based on the given time t n The predicted crack depth at a i Pre The median, standard deviation, and variance of the predicted value a are calculated.i Pre Based on the median, standard deviation and variance of the above, it is possible to accurately evaluate the remaining life span.

[0067] (4) The reference data for the probability density distribution of the measurement error is modeled using a continuous probability distribution. This configuration facilitates the design of a program to be stored in the storage device of the control device 100. Furthermore, the calculation process is simplified, reducing the calculation load.

[0068] (5) The control device 100 sets a plurality of parameters using random numbers. This configuration eliminates the need to create a data map of a plurality of analysis conditions in advance, thereby simplifying the preparation process for crack growth prediction.

[0069] (6) Crack propagation evaluation is performed based on probabilistic fracture mechanics (PFM). Therefore, the crack propagation prediction system 1 of this embodiment can quantitatively evaluate the failure frequency of the evaluation target, taking into account the uncertainty of various parameters.

[0070] The crack propagation prediction method and crack propagation prediction system 1 according to this embodiment can also be specified as follows.

[0071] (A) The crack propagation prediction method includes steps (S110, S115) of obtaining historical data of crack depth obtained by crack propagation analysis for multiple conditions (initial crack depth, propagation rate), and determining the difference da of crack depth at the same time of historical data of crack depth obtained by multiple non-destructive inspections. i A step (S120) of calculating the probability density f(da i ) and calculate the product p n and a step (S120) of calculating the product p of the probability density of all inspections under each crack analysis condition for the crack growth analysis results under all conditions. nand a step of updating the probability density of the predicted crack depth by evaluating the crack depth corresponding to the non-destructive inspection time in each crack growth analysis, thereby improving the prediction accuracy of the crack growth behavior.

[0072] (B) Inspection accuracy data in nondestructive inspection (reference data for the probability density distribution of measurement errors) is preferably expressed using a continuous probability distribution model such as a normal distribution.

[0073] (C) The crack propagation prediction method includes a step (S135) of performing a crack propagation evaluation based on probabilistic fracture mechanics using probability information about the predicted crack depth, thereby enabling accurate evaluation of future fatigue crack propagation behavior.

[0074] (D) The crack propagation prediction system 1 includes a non-destructive testing unit 103 that measures crack depths by non-destructive testing at any timing and stores the results in a history database; an operation history recording unit 101 that saves operation data of the equipment to be evaluated; a crack propagation analysis unit 102 that sets initial crack dimensions within any range using random numbers in the crack occurrence area and performs crack propagation analysis under multiple conditions taking into account variations in crack propagation speed and stress conditions using the Monte Carlo method or the like to evaluate crack propagation behavior; and a non-destructive testing unit 103 that performs a test under conditions equivalent to the timing at which the equipment to be evaluated is inspected. The system includes a crack dimension error evaluation unit 104 that compares the difference between the crack dimension obtained by the non-destructive testing unit 103 and the crack dimension analysis result obtained by the crack propagation analysis unit 102 at the evaluation target position, an error update unit 142 that evaluates the probability density of the evaluation error in each crack propagation analysis result based on the non-destructive testing accuracy database 133 and updates the predicted error of the crack dimension at the current time, a crack propagation evaluation unit 105 that evaluates the remaining life by re-evaluating the crack propagation behavior based on the updated error distribution, and a result output unit 106 that outputs the crack propagation evaluation result.

[0075] (E) The crack propagation prediction system 1 models the measurement error of the crack size in the non-destructive testing accuracy database 133 with a continuous probability distribution such as a normal distribution, and updates the posterior probability density distribution by Bayesian updating every time the crack size is measured by the non-destructive testing unit 103. This improves the evaluation accuracy of the crack propagation behavior.

[0076] (F) The crack propagation analysis unit 102 performs crack propagation calculations for N cases according to the operating conditions, and calculates the calculated crack dimensions (a i Cal ) is the median value, and the crack size (a i Insp ) and the difference da i Calculate the probability density distribution of the measurement error obtained from the nondestructive testing accuracy database 133, and use it to calculate the product of the probability density p n Calculate the predicted value a from the evaluation results of all N cases. i Pre Update the median and variance of

[0077] (G) Permanent non-destructive testing equipment is installed for crack size measurement in the non-destructive testing section 103, and crack sizes are constantly monitored during operation of the equipment. This allows the crack growth strength to be re-evaluated every time a non-destructive test is automatically performed in the non-destructive testing section 103, resulting in highly accurate evaluation results.

[0078] The following modified examples are also within the scope of the present invention, and it is possible to combine the configuration shown in the modified example with the configuration described in the above embodiment, or to combine the configurations described in the different modified examples below.

[0079] <Variation 1> In the above embodiment, an example has been described in which the crack growth analysis unit 102 performs a crack growth evaluation based on the calculation result of the stress intensity factor using the simplified evaluation formula, but the present invention is not limited to this. For example, the crack growth analysis unit 102 may perform a crack growth evaluation using finite element analysis or an extended finite element method to achieve a more accurate evaluation.

[0080] <Variation 2> In the above embodiment, an example has been described in which the crack propagation analysis unit 102 uses random numbers to set multiple cases (analysis conditions) in which at least one of multiple parameters including the initial crack depth and the crack propagation rate is different, but the present invention is not limited to this. A data map in which multiple analysis conditions are stored in advance in a storage device may also be stored.

[0081] <Variation 3> In the above embodiment, an example has been described in which the inspection device 4 monitors the depth of a crack while the equipment to be evaluated is in operation, but the present invention is not limited to this. The inspection device 4 may be a temporary non-destructive inspection device. In this case, the depth of a crack is measured at any timing, and the measurement time and the measurement value are input to the control device 100.

[0082] <Variation 4> In the above embodiment, an example has been described in which the control device 100 updates the probability density distribution every time it acquires a measured value of the crack depth. However, the timing of updating the probability density distribution may be set to any timing. In this case, the process shown in the flowchart of FIG. 2 starts when a signal requesting execution of a crack growth analysis is input from the external device (input device) 5.

[0083] <Variation 5> The function of the crack measurement unit 131 of the control device 100 may be provided in the inspection device 4.

[0084] <Variation 6> In the above embodiment, an example has been described in which the results of the crack growth evaluation are output by the display device 2, but the present invention is not limited to this. The output device that outputs the results of the crack growth evaluation may be a printing device, a communication device, or the like.

[0085] Although the embodiments of the present invention have been described above, the above embodiments merely illustrate some of the application examples of the present invention, and it is not intended that the technical scope of the present invention be limited to the specific configurations of the above embodiments. [Explanation of symbols]

[0086] 1...crack propagation prediction system, 2...display device (output device), 4...inspection device, 5...external device (input device), 100...control device, 101...operation history recording unit, 102...crack propagation analysis unit, 103...non-destructive testing unit, 104...crack dimensional error evaluation unit, 105...crack propagation evaluation unit, 106...result output unit, 121...basic condition setting unit, 122...random number generation unit, 123...evaluation database, 124...analysis condition setting unit, 125...crack propagation calculation unit, 131...crack measurement unit, 132...measurement result database, 133...non-destructive testing accuracy database, 141...dimensional error evaluation unit, 142...error update unit, a i Cal …analytical value of crack depth, a i Insp …crack depth measurement, a i Pre …predicted crack depth, da i …Error (difference), f(da i )... probability density, Di... probability density distribution, i... measurement point, N... number of analysis trials (number of studies, number of evaluations, number of analysis conditions)

Claims

1. A crack growth prediction system including a control device that performs crack growth evaluation of an evaluation target device, The control device Obtaining actual measurement data that correlates the crack depth measurement value obtained by non-destructive testing with the time of measurement; performing a crack growth analysis for each of a plurality of analysis conditions in which at least one of a plurality of parameters including an initial value of the crack depth and a crack growth rate is different, and calculating an analysis value of the crack depth for each of the plurality of time points for each of the plurality of analysis conditions; calculating a difference between the analytical value and the measured value of the depth of the crack for each of the plurality of time points; calculating a probability density based on the calculated difference and predetermined reference data of a probability density distribution of measurement errors by non-destructive testing; updating a probability density distribution of the depth of the crack based on the probability densities calculated at each of the plurality of time points; performing a crack growth assessment based on the updated probability density distribution of the crack depth; outputting the results of the crack growth evaluation; Crack growth prediction system.

2. The crack growth prediction system according to claim 1, further comprising an inspection device that performs a non-destructive inspection of the evaluation target device while the evaluation target device is in operation; The control device During operation of the evaluation target equipment, the measurement value of the crack depth is obtained by calculating the measurement value of the crack depth based on the inspection result of the inspection device; updating the probability density distribution of the crack depth each time a new measurement value is obtained; Crack growth prediction system.

3. The crack growth prediction system according to claim 1, The control device calculating a difference between the analysis value of the crack depth calculated for each of a plurality of analysis conditions and the measured value of the crack depth obtained by the non-destructive inspection; calculating the probability density based on the calculated difference and the reference data of the probability density distribution of the measurement error; calculating a sum of the probability densities calculated for each of the time points up to a predetermined time point for each of a plurality of analysis conditions; calculating a median and a variance of the predicted value of the crack depth at the predetermined time point based on the sum of the probability densities calculated for each of the plurality of analysis conditions and the analysis value of the crack depth; Crack growth prediction system.

4. The crack growth prediction system according to claim 1, the reference data of the probability density distribution of the measurement error is modeled by a continuous probability distribution; Crack growth prediction system.

5. The crack growth prediction system according to claim 1, the control device sets the plurality of parameters using random numbers; Crack growth prediction system.

6. The crack growth prediction system according to claim 1, The crack growth assessment is performed based on probabilistic fracture mechanics. Crack growth prediction system.

7. acquiring actual measurement data in which the measurement value of the crack depth obtained by the non-destructive testing performed on the evaluation target equipment is associated with the time point at which the measurement was made; performing a crack propagation analysis for each of a plurality of analysis conditions in which at least one of a plurality of parameters including an initial value of the crack depth and a crack propagation rate is different, and calculating an analysis value of the crack depth for each of the plurality of time points for each of the plurality of analysis conditions; calculating a difference between the analytical value and the measured value of the depth of the crack for each of the plurality of time points; calculating a probability density based on the calculated difference and predetermined reference data of a probability density distribution of measurement errors by non-destructive testing; updating a probability density distribution of the crack depth based on the probability densities calculated for each of the plurality of time points; performing a crack growth assessment based on the updated probability density distribution of the crack depth; and outputting the results of the crack growth assessment. Crack growth prediction method.

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