Water turbine laser cladding layer quality evaluation method

Abstract

The invention relates to the field of laser cladding layer quality evaluation, and discloses a water turbine laser cladding layer quality evaluation method which comprises the following steps: acquiring ultrasonic waveform data of a water turbine laser cladding layer; the joint posterior probability distribution comprises a residual stress field and a microscopic damage field in the cladding layer at the same time, and the joint posterior probability distribution is obtained through a forward physical operator coupled with a nonlinear acoustic elastic model and a microscopic mechanical model; the residual stress field and the microscopic damage field are associated with the ultrasonic waveform data. The residual stress field and the microcosmic damage field are deeply coupled on the physical model level to realize synchronous solution of the residual stress field and the microcosmic damage field, so that compared with a scheme in the prior art that stress and damage are separated, and one of the stress and the damage is evaluated or ignored, the method has the advantages that the reliability is high; according to the method, the problems of blurring evaluation results and insufficient reliability caused by confusion of physical effects are solved.

Description

Technical Field

[0001] The present invention relates to the field of laser cladding layer quality evaluation, and specifically to a method for evaluating the quality of a laser cladding layer on a hydraulic turbine. Background Art

[0002] A hydraulic turbine is the core equipment for hydropower generation. Its flow-through components, such as runner blades, work under the erosion and cavitation of high-speed sand-laden water for a long time, and the surface is prone to damage. To extend its service life and repair damaged components, laser cladding technology, as an advanced surface remanufacturing method, has been widely used. This technology coats a layer of metal ceramic or alloy with high hardness and high wear resistance on the component surface to resist damage. Therefore, accurate and reliable non-destructive evaluation of the internal quality of the laser cladding layer is a key link to ensure the safe, stable and long-term operation of the hydraulic turbine. At present, the evaluation of the cladding layer quality mainly relies on various non-destructive testing technologies. Among them, ultrasonic testing has become the main method because of its strong penetration ability and sensitivity to internal defects, and it is often supplemented by X-ray diffraction method for residual stress analysis, or by metallographic analysis for microstructural characterization.

[0003] However, when the existing technology is applied to the quality evaluation of laser cladding layers on hydraulic turbines under such complex working conditions, there are still some inherent technical limitations. In the cladding layer, the residual stress generated by the rapid solidification process and the inevitable microstructural metallurgical defects (pores, microcracks) are two coexisting and intertwined key physical states. Both of these states will disturb the propagation of ultrasonic waves, resulting in changes in their acoustic signal characteristics, which constitutes a physical coupling and confusion. Therefore, any method that attempts to measure only one of these physical quantities will inevitably be interfered by the other physical quantity, making the source of the evaluation result unclear. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the present invention provides a method for evaluating the quality of a laser cladding layer on a hydraulic turbine, which solves the problems in the existing technology that it is difficult to synchronously decouple and independently evaluate due to the physical effects of residual stress and microdamage being coupled with each other, and the evaluation result is usually a single determined value and cannot quantify its own uncertainty.

[0005] To achieve the above objectives, the present invention is realized through the following technical solutions: A method for evaluating the quality of a laser cladding layer on a hydraulic turbine, comprising the following steps:

[0006] Obtain the ultrasonic waveform data of the laser cladding layer of the water turbine; this process is the physical information input end of the entire evaluation system. The mechanism is that any physical inhomogeneity existing inside the cladding layer, whether it is the non-linear response of the material caused by residual stress or the acoustic impedance mismatch caused by micro-damage, will disturb the propagation path, speed and shape of the ultrasonic wave passing through it. By collecting the complete time-domain waveform signal, rather than a single characteristic parameter, the rich details imprinted on the acoustic wave by the internal state can be retained to the greatest extent, providing the most original and complete physical evidence for subsequent analysis.

[0007] Establish a joint posterior probability distribution that simultaneously includes a residual stress field and a micro-damage field inside the cladding layer. Among them, the joint posterior probability distribution correlates the residual stress field and the micro-damage field with the ultrasonic waveform data through a forward physical operator that couples a non-linear acoustoelastic model and a micro-mechanics model;

[0008] First of all, as a bottom-layer module, the micro-mechanics model converts the discrete, micro-scale damage information (porosity) into the influence on the macroscopic equivalent elastic properties of the material. Its role is to define a virtual medium that becomes inhomogeneous due to damage;

[0009] Subsequently, as an upper-layer module, the non-linear acoustoelastic model further superimposes the non-linear influence of the residual stress field on the acoustic wave propagation speed on the basis of this virtual medium. The coupling relationship between these two models accurately simulates the real situation where stress and damage physically coexist and act on the acoustic wave simultaneously. Therefore, this forward physical operator constitutes a virtual simulation channel from the "hypothetical internal state" to the "predicted acoustic response", which provides a physical criterion for measuring the matching degree between any set of hypothetical fields and the real observation data.

[0010] Adopt a Markov chain Monte Carlo algorithm that utilizes gradient information to numerically sample the joint posterior probability distribution to obtain a solution ensemble of the residual stress field and the micro-damage field;

[0011] Since the shape of the posterior probability distribution is extremely complex and in a high-dimensional space, it cannot be directly solved, so an intelligent exploration tool is needed. An algorithm that utilizes gradient information has a different mechanism of action from blind random search. It can sense the "topographic slope" of the probability distribution in the parameter space, i.e., the gradient. This enables the algorithm to efficiently move towards regions with higher probabilities, thus greatly enhancing the efficiency and robustness of finding all high-likelihood solutions in the high-dimensional space. The product of this process is not a single solution, but an ensemble of solutions consisting of thousands of valid solution samples. Each sample in this ensemble of solutions is a reasonable "snapshot" of the true state inside the clad layer, and the entire set constitutes a discretized approximation of the posterior probability distribution, which is a bridge connecting the abstract mathematical model and the specific physical analysis.

[0012] Perform statistical analysis on the ensemble of solutions to generate a probabilistic quality assessment result of the clad layer that includes uncertainty quantification information.

[0013] Through statistical refinement of the huge data set of the ensemble of solutions, the information hidden therein is transformed into understandable engineering conclusions. By calculating the average value of all samples, the best estimates of the stress field and damage field can be obtained; more importantly, by analyzing the dispersion or range of variation between samples, the uncertainty of the assessment result at each spatial location point can be directly quantified. This uncertainty information is endogenous to this method rather than externally added, and it directly reflects the reliability of the model inference under the current observed data. The finally generated probabilistic assessment result integrates this best estimate with the uncertainty information, completing the complete information chain from the original acoustic signal to the final quantified risk assessment.

[0014] Preferably, the steps for obtaining the ultrasonic waveform data of the laser clad layer of the water turbine include:

[0015] Use an ultrasonic phased array probe to perform full matrix capture scanning on the area to be evaluated of the clad layer to obtain a full matrix waveform data set.

[0016] The ultrasonic phased array probe here is a key hardware component. It is not a single vibrating element, but an array of multiple independent and individually controllable piezoelectric wafer elements integrated in a probe housing. Its working mechanism is that by precisely controlling the excitation and reception timing of each element, it has the ability to flexibly shape the sound field. However, in this method, its more core role is as a high-throughput multi-channel data acquisition front end.

[0017] On this basis, the Full Matrix Capture (FMC) scan performed is a specific data acquisition strategy. Its mechanism lies in the pursuit of the completeness of information capture. The specific operation process is as follows: First, the system instructs the first element in the probe to emit a beam of ultrasonic waves. At the same time, all elements in the probe, including the transmitting element, switch to the receiving mode and synchronously record the complete waveform signals they receive and return over time. After this process is completed, the system automatically switches, with the second element serving as the transmitting source, and again all elements receive. This process loops in sequence until each element has completed one operation as the transmitting source.

[0018] The deep mechanism of this strategy is that it systematically records all the acoustic wave propagation paths between any two elements in the probe. The finally obtained full matrix waveform data set is a huge information collection containing N times N groups (N is the total number of elements) of independent waveform signals. This data set not only contains the signals of acoustic waves propagating along straight paths, but more importantly, it also completely captures the signals formed after the complex phenomena of scattering, diffraction, and mode conversion occur when acoustic waves encounter the residual stress area or microscopic damage bodies inside the cladding layer. Through this exhaustive acquisition method, acoustic waves from different paths "examine" the same internal feature from different angles, thus forming a very high degree of information redundancy and complementarity at the data level. It is precisely this great abundance of information that provides the necessary data basis for subsequent algorithms to attempt to separate the weak perturbations of the two different physical sources of stress and damage from the confused signals. This data set constitutes the only and complete experimental input for all subsequent physical modeling and statistical inferences.

[0019] Preferably, before establishing the joint posterior probability distribution, it further includes:

[0020] Using the Karhunen - Loève expansion method, parameterize the residual stress field and the microscopic damage field into random variable vectors of finite dimensions respectively.

[0021] The necessity of this step is that a continuous physical field, a stress field with numerical values at each point in the three - dimensional space of the cladding layer, is a mathematically infinite - dimensional object. If we want to directly solve it on a computer, we need to deal with infinitely many unknowns, which is computationally infeasible.

[0022] The mechanism of the Karhunen-Loève (KL) expansion is an efficient dimensionality reduction. It decomposes a complex, continuously distributed field function into a linear combination of a set of predetermined, fixed spatial basis functions and a set of uncorrelated random variable coefficients to be solved. These spatial basis functions are like the "building blocks" for constructing the physical field. They contain prior information about the spatial distribution characteristics of the physical field and can be constructed to efficiently represent smooth or fields with specific spatial correlations.

[0023] Specifically, this method transforms the stress values and damage values that originally needed to be solved at thousands of grid nodes in space into a problem that only requires solving a few (from dozens to hundreds) of random variable coefficients. These random variable coefficients form a finite-dimensional vector, and the subsequent solution process will be completely carried out in this low-dimensional parameter space, rather than directly dealing with the high-dimensional physical field space.

[0024] This step is a key bridge connecting physical modeling and numerical calculation. It greatly reduces the solution dimension of the problem while maintaining a sufficiently high-fidelity description of the original physical field. This parameterization process successfully transforms an infinite-dimensional functional inversion problem into a well-defined and computationally feasible finite-dimensional parameter estimation problem.

[0025] Preferably, the joint posterior probability distribution is determined by Bayes' theorem:

[0026] ;

[0027] where is a random variable vector characterizing the residual stress field and the micro-damage field, is the acquired ultrasonic waveform data, is the likelihood function derived from the forward physical operator, is the prior probability distribution of the random variable vector.

[0028] The ultimate goal in this framework is to obtain a "posterior probability distribution". It represents our final and most comprehensive understanding of the unknown state inside the cladding layer (represented by the parameterized random variable vector) after obtaining all experimental observation data. It is not a single numerical solution, but a complete probability blueprint that describes all possibilities and their corresponding credibility.

[0029] To construct this posterior probability distribution, two key input modules are required.

[0030] The first input module is the "likelihood function". Its mechanism of action is to serve as a bridge connecting the physical world and the abstract model. This function is derived from the previously established complex forward physical operator. If a parameter combination can predict a waveform that highly matches the real observation, then the corresponding likelihood function value is high; otherwise, it is low. Therefore, the likelihood function is essentially a physical model-based quantitative indicator for measuring the "model-data" matching degree.

[0031] The second input module is the "prior probability distribution". Its mechanism of action is to act as a knowledge container, injecting all the background information or physical constraints about the unknown parameters known before the experimental observation into the model in mathematical language. Engineering experience tells us that the residual stress field usually changes smoothly, or the microdamage value cannot be negative. The prior probability distribution encodes this "common sense" or expert-level knowledge, and it plays the role of a "navigator" or "stabilizer" throughout the solution process, guiding the solution process towards a more physically reasonable direction and avoiding meaningless or physically counterintuitive solutions.

[0032] Finally, the mechanism of action of Bayes' theorem is to logically multiply these two modules. It uses the "matching degree map" (likelihood function) representing experimental evidence to point-by-point correct and update the "initial belief map" (prior distribution) representing prior knowledge, and finally generates the "final cognitive map" (posterior distribution) containing all information. This posterior distribution is the culmination of all available information - including physical laws, prior knowledge, and experimental data - and is the core mathematical object pursued by the entire evaluation method.

[0033] Preferably, the forward physical operator takes the random variable vector as input, and its internal operations include:

[0034] According to the reconstruct the residual stress field and the microdamage field;

[0035] Apply the micromechanics model to calculate an equivalent elastic tensor based on the microdamage field;

[0036] Apply the nonlinear acoustoelastic model to calculate an acoustoelastic tensor based on the equivalent elastic tensor and the residual stress field, and predict the ultrasonic waveform data accordingly.

[0037] The first stage of the operation is "decoding and reconstruction". The mechanism is to inversely transform the input low-dimensional abstract parameter vector into a physically understandable specific physical field distributed over the entire three-dimensional computational domain. This process generates two independent fields: one is the residual stress tensor field, and the other is the microscopic damage scalar field. This step is the starting point of the entire simulation process, which concretizes a pure mathematical assumption into a complete and imaginary physical state inside the cladding layer.

[0038] The second stage of the operation is "macroscopicization of damage effects". It receives the microscopic damage field generated in the first stage as input and processes it using a micromechanics model. The mechanism of this model is that it can calculate the comprehensive influence of these microscopic defects on the macroscopic elastic properties of the material based on the local density and morphology of the microscopic damage (pores or microcracks). The output of this module is a new and non-uniform equivalent elastic tensor. This tensor no longer describes an ideal and intact matrix material, but a virtual medium with spatially varying stiffness due to internal damage. This module is the unit in the entire operator specifically responsible for simulating damage effects.

[0039] The third stage of the operation is "superposition of stress effects and final simulation". This stage is the core of the physical simulation, which couples the results of the previous two stages. It receives two inputs: one is the equivalent elastic tensor calculated in the second stage that already includes damage effects, and the other is the residual stress field reconstructed in the first stage. On this basis, it applies a nonlinear acoustoelastic model. The mechanism of this model is to describe the physical phenomenon of how the acoustic wave propagation speed is affected by the stress state. It superimposes the action of the stress field on the material that already takes damage into account, and finally calculates a final acoustoelastic tensor that simultaneously includes the dual effects of stress and damage. This final tensor is the most complete physical property description of this virtual cladding layer under a certain assumed state. Subsequently, the operator simulates the entire process of ultrasonic wave emission, propagation, and reception in a virtual environment that is exactly the same as the real experiment based on this final property, so as to predict the final ultrasonic waveform data. This predicted data is the final output of the entire forward physical operator.

[0040] Preferably, the micromechanics model is the Mori-Tanaka model.

[0041] When the Mori-Tanaka model is selected, its core mechanism is that it provides an efficient and physically meaningful way to estimate the macroscopic equivalent elastic properties of materials containing randomly distributed microscopic defects. This model regards the cladding layer as a composite material, in which the intact metal matrix is regarded as the "matrix phase", and the internal microscopic pores or microcracks are regarded as the "inclusion phase".

[0042] The internal working mechanism of this model is based on the mean field theory. It first analyzes the stress field and strain field perturbations caused by a single inclusion (a micropore) in an infinitely large matrix. Subsequently, the essence of the Mori-Tanaka model lies in that it considers the interactions among numerous inclusions through a clever approximation: it assumes that each independent inclusion does not exist in isolation in a pure matrix, but in an equivalent medium that has been "pre-perturbed" by the average influence of all other inclusions.

[0043] Through this "mean field" idea, the model can estimate the average stress and strain borne by the matrix phase and all inclusion phases when an external load is applied. Based on these mean field quantities, the model can then derive a macroscopic, homogenized equivalent elastic tensor that can represent the entire damaged material region.

[0044] Therefore, the role of the Mori-Tanaka model in this method is a dedicated "translation module". It receives the scalar field (porosity distribution map) provided by the upstream module that describes how microdamage is distributed in space, and accurately "translates" it into an equivalent elastic tensor field that the downstream nonlinear acoustoelastic model can understand and that describes the change in the macroscopic mechanical response of the material. This translation process is a key link connecting the microstructure and macroscopic physical properties, and it quantitatively answers the core question of "how much does a specific degree of damage actually affect the acoustic stiffness of the material".

[0045] Preferably, the Markov chain Monte Carlo algorithm using gradient information is the Hamiltonian Monte Carlo algorithm.

[0046] The mechanism for choosing this algorithm is that the posterior probability distribution faced by this method usually exists in a parameter space with extremely high dimensions and complex shapes. Traditional random walk sampling algorithms are extremely inefficient in such spaces, like a blind person randomly taking steps in a vast mountain range, easily getting lost in the "plain" with lower probabilities or being trapped in a local "valley".

[0047] The mechanism of action of the Hamiltonian Monte Carlo (HMC) algorithm is completely different. It provides a much more intelligent exploration strategy. It cleverly analogizes a pure mathematical sampling problem to a dynamic system defined in classical physics. In this virtual physical system, the unknown parameter vector to be solved is regarded as the "position" of a particle, and the "potential energy" at the position of this particle is directly defined by the target posterior probability distribution - the regions with higher probabilities correspond to the "valleys" with lower potential energies.

[0048] The most core innovation of this algorithm lies in that it introduces an auxiliary "momentum" variable for this particle. The role of this momentum is to endow the particle with inertia. Therefore, the sampling process of the algorithm is no longer a random jump without direction, but generates new sample proposals by simulating the movement of this particle in the potential energy field. It first gives the particle a random initial momentum (a random "thrust"), and then allows the particle to slide along the trajectory of energy conservation for a preset time. Due to the existence of momentum, the particle can make long-distance and coherent movements, efficiently exploring the vast space of the probability distribution, especially along the narrow "valley" areas.

[0049] This exploration method based on physical dynamics enables the algorithm to utilize the gradient information of the probability distribution (i.e., the "slope of the terrain") to guide its moving direction, thereby finding and extracting samples from all high-probability regions in the complex high-dimensional space with far higher efficiency than traditional methods, providing a solid computational guarantee for obtaining reliable evaluation results.

[0050] Preferably, the gradient information of the joint posterior probability distribution required by the Hamiltonian Monte Carlo algorithm is calculated by establishing an adjoint state method solver for the forward physical operator.

[0051] The efficiency of the Hamiltonian Monte Carlo algorithm completely depends on its ability to obtain the gradient of the target probability distribution at any point, that is, the "slope of the terrain". However, this gradient information is deeply hidden inside the extremely complex forward physical operator that relates the unknown parameters to the ultrasonic data. If conventional numerical methods (finite difference method) are used to calculate the gradient, its mechanism is equivalent to measuring the slope of a mountain at a certain point. One needs to stand at that point first, and then take a small step in each of the east-west, north-south directions and record the height change each time. For a high-dimensional problem with hundreds or thousands of unknown parameters, this means that in order to obtain a complete gradient information, the time-consuming forward physical simulation needs to be run hundreds or even thousands of times, which is completely infeasible computationally.

[0052] The adjoint state method provides an elegant solution with a completely different mechanism to fundamentally solve this problem. It does not observe the output by repeatedly perturbing the input, but directly calculates the gradient by analyzing the information flow inside the system.

[0053] Its core mechanism of action is that it works by solving a brand new "adjoint process" that is mathematically related to the original physical process (i.e., the forward process). This adjoint process can be understood as the reverse propagation of the causal chain in the original physical process. The forward process simulates the information flow from "internal state" to "external observation", while the adjoint process simulates a virtual information flow that traces back from "deviation of external observation" to "the source of the internal state that caused the deviation".

[0054] Specifically, the method establishes a corresponding adjoint solver for that complex multiphysics forward operator. When the gradient needs to be calculated, the system first performs a forward simulation to obtain the predicted waveform and calculate the difference between it and the actual observed waveform. Then, the adjoint solver uses this difference as its "stimulus source" and starts to perform an adjoint simulation. The final output of this adjoint simulation gives the sensitivity of the final waveform difference to all the initial unknown parameters at once and simultaneously, that is, the complete gradient vector.

[0055] The key advantage of this method is that the computational cost of performing an adjoint simulation is roughly equivalent to the cost of performing a forward simulation. This means that no matter how high the dimensionality of the unknown parameters is, this method can obtain complete gradient information at the computational cost of about two forward simulations. Therefore, this adjoint state method solver plays the role of an efficient "gradient engine" in this method. As an underlying core module serving the Hamiltonian Monte Carlo algorithm, it provides it with a steady stream of cheap and accurate gradient information, making it possible to perform robust Bayesian inference in extremely high-dimensional parameter spaces.

[0056] Preferably, the step of performing statistical analysis on the solution ensemble comprises:

[0057] reconstructing a plurality of residual stress field samples and microscopic damage field samples from the solution ensemble;

[0058] The a posteriori expectation field and the a posteriori variance field of the residual stress field and the microscopic damage field are calculated, wherein the a posteriori variance field is used to quantify the uncertainty.

[0059] This analysis process first includes reconstructing multiple residual stress field samples and micro-damage field samples from the solution ensemble. The mechanism of this step lies in "decoding". The previous Monte Carlo algorithm explores and samples in a reduced-dimensional and abstract parameter space, and its direct product (i.e., the solution ensemble) is a series of low-dimensional random variable vectors. These vectors themselves do not have intuitive physical meanings. Therefore, as a decoding module, this reconstruction step maps each random variable vector sample one by one through an inverse transformation (Callanan-Loewe inverse expansion) back to its uniquely corresponding field function distributed in the complete three-dimensional physical space. After this process, we obtain thousands of specific "snapshots" of the residual stress field and "snapshots" of the micro-damage field, which together constitute a complete probabilistic description of the true internal state of the cladding layer, preparing the most direct physical input for subsequent statistical analysis.

[0060] After obtaining this set of field samples, the next step in the analysis is to calculate the posterior expected fields and posterior variance fields of the residual stress field and the micro-damage field.

[0061] The calculation of the posterior expected field is based on the mechanism of extracting the "consensus" or "central tendency" among all possibilities. By averaging all field samples at each spatial position point by point, a single and smooth physical field can be obtained. This posterior expected field represents the best point estimate of the true physical field based on all available information (including prior knowledge and experimental data), and it is the solution that is most likely to be close to the real situation in a probabilistic sense.

[0062] At the same time, the posterior variance field is calculated. Its mechanism lies in self-examining and quantifying the credibility of the evaluation results themselves. The magnitude of the variance directly reflects the degree of dispersion among all field samples at a specific spatial position point. If the variance value at a certain point is large, it means that different samples give very different predicted values at this point, indicating that the existing observational data do not provide strong enough constraints on the state of this point, so the evaluation result has a high degree of uncertainty here. On the contrary, a very small variance value represents that all samples tend to be consistent, indicating that the model has high confidence in the evaluation result at this point. Therefore, this posterior variance field, as a core output module, serves to generate an intuitive "uncertainty map", which transforms uncertainty from a vague concept into a physical quantity that can be precisely quantified and spatially visualized, and this is the key to the probabilistic evaluation of this method.

[0063] Preferably, the statistical analysis further includes:

[0064] Calculating the posterior probability distribution of at least one key quality indicator and determining a risk probability that the key quality indicator exceeds a preset safety threshold according to this distribution.

[0065] A scalar derived from the complete field evaluation results with clear engineering significance. It is not a distributed field but a single numerical value, such as the "peak tensile stress" within the entire clad layer area or the "average porosity" in a certain key sub-region. These metrics are often directly related to the failure modes or life predictions of structural components. The role of this calculation module is to extract the numerical values of these key metrics one by one from the thousands of previously generated stress field or damage field samples. It will traverse each stress field sample to find the maximum tensile stress value in that sample.

[0066] After this process, the product is no longer a set of fields but a new set consisting of thousands of numerical values of key quality metrics. This numerical set itself is a complete and discrete description of the posterior probability distribution of this key quality metric. It clearly shows, in the form of a histogram, the range of all possible values of this key metric and the relative likelihood of each value after integrating all information.

[0067] After obtaining this posterior probability distribution, the final analysis step is to determine a risk probability that the key quality metric exceeds a preset safety threshold based on this distribution.

[0068] The mechanism of this step lies in directly colliding and comparing probability analysis with engineering specifications. The "preset safety threshold" here is a critical value defined by engineering design standards, material property limits, or safety regulations, such as the yield strength of the material or an acceptable maximum defect size. The operation performed by this calculation module is very intuitive: it will systematically check the set of numerical values of the key quality metrics generated in the previous step and count how many of these values fall on the "dangerous" side of this safety threshold.

[0069] Ultimately, the risk probability is calculated by dividing the number of "exceeding the limit" samples by the total number of samples. This final output risk probability value is the ultimate output of the entire evaluation method. It condenses a complex, multi-dimensional probability assessment problem into a single, extremely user-friendly percentage value for decision-makers. It no longer merely answers "what the stress might be" but directly and quantitatively answers the question "what is the probability that the component is in an unsafe state?" Therefore, this module is the last link connecting scientific analysis and risk management, providing the most direct and core decision-making basis for implementing risk-based maintenance strategies or conducting lean quality control.

[0070] The present invention provides a method for evaluating the quality of a laser clad layer of a water turbine. It has the following beneficial effects:

[0071] 1. The present invention adopts a unified probabilistic inversion framework, deeply coupling the residual stress field and the microdamage field at the physical model level to achieve synchronous solution of the two. This solution can obtain a more complete and physically self-consistent characterization of the internal state of the cladding layer. Compared with the prior art solutions that separate stress and damage and evaluate them separately or ignore one of them, the present invention solves the problem of unclear evaluation results and insufficient reliability caused by the confusion of physical effects.

[0072] 2. The present invention introduces a complete Bayesian statistical inference process, and its evaluation result is not a single definite value, but a probabilistic physical field including posterior expectation and posterior variance. This method can clearly reveal the reliability degree of the evaluation result everywhere in space. It overcomes the limitation of traditional non-destructive testing techniques that only provide a deterministic result and cannot reflect the uncertainty of the result, and solves the problem of giving false sense of security to decision-makers or causing over-conservative maintenance.

[0073] 3. The present invention integrates an efficient field parameterization method and a gradient-based Monte Carlo sampling algorithm, and equips it with a dedicated adjoint state solver. This achieves an effective solution to the inverse problem of high-dimensional complex physical fields in terms of calculation. Compared with the prior art solutions that are forced to simplify the model or reduce the resolution due to huge computational cost when facing such problems, the present invention solves the dilemma of being difficult to balance physical authenticity and computational feasibility.

[0074] 4. The method system of the present invention can finally output the specific risk probability that the key quality index exceeds the safety threshold. It directly transforms the complex field quantity analysis into a clear and quantifiable risk index that can be used for engineering decision-making. This approach solves the defect that the uncertainty accumulates in the information transmission chain and cannot be effectively quantified in the prior art process where measurement and risk assessment are disjointed and require multi-step indirect analysis, ultimately resulting in low transparency and credibility of risk assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0076] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0077] Embodiment:

[0078] Please refer to the attachedFigure 1 , an embodiment of the present invention provides a method for evaluating the quality of a laser cladding layer of a water turbine, including:

[0079] S1. In this embodiment, the first step of the evaluation method of the present invention is to obtain full matrix capture (FMC) ultrasonic waveform data of the cladding layer. This step aims to collect original acoustic signals with high signal-to-noise ratio and high information redundancy to provide sufficient experimental input for subsequent complex inversion calculations.

[0080] Generally, the data acquisition system consists of a multi-channel ultrasonic data acquisition instrument, an ultrasonic phased array probe, and an automated precision scanning device. The ultrasonic data acquisition instrument has at least 64 parallel transmit / receive channels and has a high enough sampling frequency, not less than ten times the center frequency of the probe, to ensure that the waveform is not distorted.

[0081] As an option, the ultrasonic phased array probe is a linear array probe. The number of array elements included in the probe is optional. In some embodiments, a 64-element or 128-element probe can be used. The center frequency of the probe is selected according to the thickness and material properties of the cladding layer, usually in the range of 5 MHz to 10 MHz, and this frequency range can achieve a good balance between detection resolution and acoustic wave penetration depth.

[0082] Specifically, the data acquisition process is carried out as follows:

[0083] First, install the phased array probe on the end effector of the automated precision scanning device, and achieve good acoustic coupling between the probe and the surface of the cladding layer through water or a special coupling agent.

[0084] Subsequently, start the scanning device, and make it raster scan the area to be evaluated of the cladding layer point by point according to the preset path planning. The stepping accuracy of the scanning device is guaranteed by a high-resolution encoder to ensure that the spatial coordinates of each acquisition position are accurately recorded.

[0085] In a possible implementation, at each scanning position point, the ultrasonic data acquisition instrument performs a full matrix capture (FMC) operation. This operation follows a specific timing logic: the system first designates the first array element as the transmitting unit and activates it to emit an ultrasonic pulse; at the same time, all H array elements (including the transmitting array element itself) serve as receiving units and synchronously record the time-domain waveform signal within a preset time length. After this process is completed, the system automatically designates the second array element as the transmitting unit and repeats the above-mentioned transmitting and receiving process. This cycle is carried out in sequence until all H array elements have completed an operation as the transmitting unit.

[0086] Thus, at a single scanning position point, a complete FMC data set is collected. This data set can be represented as a three-dimensional data matrix, which contains A set of time-domain waveform signals, where is the total number of probe array elements. Each set of waveform signals has the mathematical form:

[0087] ;

[0088] where:

[0089] represents the voltage signal that varies with time emitted by the -th element and received by the -th element;

[0090] is the index of the transmitting element;

[0091] is the index of the receiving element;

[0092] is the total number of elements of the phased array probe.

[0093] As an option, to further improve the data acquisition efficiency, this step can also adopt the acquisition strategy of PlaneWaveImaging (PWI). Under this strategy, by applying specific delays to the probe array elements, a plane wavefront emitted at a specific angle (from -30 degrees to +30 degrees, with a step of 1 degree) is synthesized. For each emission of a plane wave at a certain angle, all elements synchronously receive the echo signals. Although the signal-to-noise ratio of the raw data of PWI is lower than that of FMC, its acquisition speed is significantly accelerated and can be compensated by subsequent signal processing.

[0094] After the data acquisition is completed, it is generally necessary to preprocess the original FMC data set. The preprocessing steps can optionally include: performing baseline correction on each waveform signal to eliminate the DC bias; applying a band-pass filter with a center frequency consistent with the nominal frequency of the probe to filter out the out-of-band noise; and using the encoder data recorded by the scanning device to associate and align each FMC data set with its exact spatial coordinates.

[0095] Finally, the output of this step is several preprocessed FMC data sets that are strictly corresponding to the spatial positions, denoted as . This output data completely and losslessly retains all the physical details of the interaction between the sound wave and the internal structure of the cladding layer, which is a necessary guarantee for the subsequent steps to perform accurate physical modeling and high-confidence inversion calculations.

[0096] S2. In this embodiment, the second step of the evaluation method of the present invention is to construct a parametric calculation model of the stress-damage field of the cladding layer and determine the joint posterior probability distribution of the field based on this. This step transforms a complex physical inverse problem into a parameter estimation problem that can be solved within a statistical framework through mathematical and physical modeling.

[0097] Generally, the modeling process starts with the establishment of a geometric model. The precise point cloud data of the cladding layer component to be evaluated is obtained by means of laser three-dimensional scanning, and a high-fidelity three-dimensional computer-aided design (CAD) model is constructed through reverse engineering based on this. Subsequently, this CAD model is imported into a finite element analysis software and high-quality mesh generation is performed on it to form a discretized computational domain.

[0098] In this computational domain, two continuously distributed physical fields to be solved are defined: one is the residual stress tensor field , which is a second-order tensor and has six independent stress components in a three-dimensional Cartesian coordinate system; the other is the microscopic damage field , which is a scalar field used to characterize the degree of damage such as porosity or microcrack density.

[0099] Specifically, since both of these field functions are infinite-dimensional variables, in order to enable their numerical processing on a computer, dimensionality reduction parameterization is required. In this step, the Karhunen-Loève (KL) expansion method is adopted to represent the field function as a linear combination of a set of deterministic basis functions and a set of random variables to be solved. For a general physical field , its KL expansion form is:

[0100] ;

[0101] where:

[0102] represents a physical field to be parameterized, a certain component of the damage field or the stress field;

[0103] is the spatial position vector in the computational domain;

[0104] is the prior mean field of this physical field, which can be set to zero according to experience or obtained from preliminary process simulations;

[0105] is the eigenvalue-eigenfunction pair of a preset prior covariance kernel function, and this kernel function contains prior knowledge about the spatial correlation (smoothness) of the physical field;

[0106] is a set of independent random variables that follow a standard normal distribution;

[0107] is the truncation order of the expansion, and its magnitude determines the accuracy of the model and the computational complexity;

[0108] is the index of the summation term in the expansion. It starts from 1 and numbers each mode of the expansion in sequence.

[0109] By performing the above expansions on all stress component fields and damage fields, the original infinite-dimensional problem is transformed into solving a single, finite-dimensional random variable vector containing all of the problem.

[0110] In one possible implementation, based on this parametric expression, a forward physical operator is constructed. This operator is a complex, multi-stage cascaded function whose function is to input a parameter vector and output a set of predicted FMC ultrasonic waveform data. The internal operation process of this operator includes:

[0111] First, according to the input parameter vector , using the KL inverse transform, the complete residual stress field and the microscopic damage field are reconstructed on all grid nodes in the computational domain.

[0112] Second, apply a micromechanics model, the Mori-Tanaka method, which takes the damage field as input and calculates the anisotropic equivalent elastic tensor caused by the presence of microscopic defects.

[0113] Third, substitute the equivalent elastic tensor calculated above and the reconstructed residual stress field into the constitutive relation of nonlinear acoustoelastic theory. This theory describes how stress changes the acoustic properties of the medium and finally calculates a final acoustoelastic tensor that includes both damage and stress effects.

[0114] Finally, in a virtual environment that is exactly the same as the physical experiment configuration, use high-precision numerical methods such as the Spectral Element Method or the Finite Difference Time Domain Method (FDTD) to solve the elastic wave equation with as the medium property. By simulating the entire process of FMC data acquisition, the final predicted waveform data is obtained, where is a forward physical operator.

[0115] After the forward physical operator is constructed, Bayes' theorem is applied to determine the joint posterior probability distribution of the unknown parameters . The expression of this distribution follows Bayes' formula: .

[0116] ;

[0117] where:

[0118] is the posterior probability distribution to be found, which represents the probability distribution of the unknown parameters after the observed data obtained in S1 are given;

[0119] is the prior probability distribution of the parameter . Due to the characteristics of the KL expansion, a standard multi-dimensional Gaussian distribution can be naturally set for it, where is the unit covariance matrix;

[0120] is the likelihood function, which quantifies the degree of agreement between the model-predicted data and the true observed data given a set of parameters . If the measurement noise and model error follow a Gaussian distribution with zero mean, the likelihood function can be expressed as:

[0121] ;

[0122] where is the covariance matrix of the noise, which describes the degree of uncertainty of the observed data.

[0123] So far, this step has completed the transformation from the physical problem to the mathematical model, and its final output is the complete mathematical definition of the joint posterior probability distribution. This distribution function incorporates all the information from physical laws (embodied in the forward operator ), from experimental observations (embodied in and the likelihood function), and from prior knowledge (embodied in ), providing a clear objective for the next step of numerical solution.

[0124] S3. In this embodiment, the third step of the evaluation method of the present invention is to numerically solve the combined posterior probability distribution to obtain a solution ensemble representing the residual stress field and the microdamage field. This step uses a Markov chain Monte Carlo (MCMC) method, whose purpose is not to find a single maximum point of the distribution, but to approximate its overall shape by extracting a large number of random samples from it.

[0125] Specifically, the HMC algorithm draws on the concept of Hamiltonian dynamics in physics. It introduces an auxiliary "momentum" variable with the same dimension for the parameter vector (analogous to the "position" variable in this system). Then, a Hamiltonian is defined , which is the total energy of the system and consists of two parts: potential energy and kinetic energy:

[0126] ;

[0127] where:

[0128] is the potential energy of the system, which is defined as the negative logarithm of the posterior probability. This is the core link connecting the physical system with the current statistical problem: .

[0129] is the kinetic energy of the system, usually defined in quadratic form: ;

[0130] where, is a symmetric positive definite mass matrix, which can be simplified to the identity matrix I in some embodiments. The momentum variable is randomly drawn from a zero-mean Gaussian distribution corresponding to the kinetic energy form, i.e., .

[0131] In a possible implementation, the HMC algorithm generates new sample proposals by simulating the evolution of this Hamiltonian system over time. In theory, in a frictionless system, the total energy is conserved. The algorithm simulates the particle starting from the current position , moving in the potential energy field for a preset time, and arriving at a new position . Due to errors in numerical integration, this process is not completely energy-conserving, so a Metropolis-Hastings acceptance step is required at the end to precisely correct the errors and ensure that the sampling finally converges to the target distribution.

[0132] The effective operation of the HMC algorithm hinges on the efficient calculation of the gradient of the potential energy field, which drives the evolution of Hamiltonian dynamics. According to the definition of potential energy, its gradient is: , and this gradient drives the evolution of Hamiltonian dynamics. According to the definition of potential energy, its gradient is:

[0133] ;

[0134] where the gradient of the prior term usually has an analytical form and is easy to calculate. The challenge lies in calculating the first part of the gradient of the log-likelihood function because it involves differentiating the extremely complex forward physical operator defined in S2.

[0135] As an option to address this challenge, this step develops and implements an Adjoint-State Method solver for the forward physical operator . The Adjoint-State Method is a technique for efficiently calculating the gradients of large-scale models. By solving an adjoint process related to the original physical process (forward process), it can obtain the gradients of the likelihood function with respect to the entire parameter vector at once, at a cost of approximately two forward model calculations. This computational efficiency is essentially independent of the parameter dimension , thus enabling the application of the HMC algorithm to the high-dimensional parameter problems involved in this invention.

[0136] During the algorithm execution phase, multiple parallel Markov chains are initialized and run simultaneously, four chains in this case. By monitoring in real-time a diagnostic metric called the Gelman-Rubin statistic (denoted as ), it is determined whether all chains have converged to the same stationary distribution. When the values of all parameters approach 1 (less than 1.01), it can be considered that the chains have converged.

[0137] The initial phase of the algorithm's operation is called the "burn-in period" or "warm-up period", and the samples in this phase are discarded because the chains have not yet forgotten their initial states. After the chains converge, the algorithm continues to run and the subsequently generated samples are collected.

[0138] Finally, the output of this step is a set containing a large number (tens of thousands) of parameter vector samples . This sample set is a discrete, numerical approximation of the target posterior probability distribution , which constitutes the so-called "solution ensemble". This solution ensemble is the key connecting the abstract probability model to the final physical interpretation, providing a complete statistical basis for subsequent quantitative analysis and evaluation.

[0139] S4. In this embodiment, statistical analysis is performed on the solution ensemble to generate a probabilistic quality assessment result of the cladding layer. The core task of this step is to convert the sample data output by the MCMC algorithm into a quantitative assessment of the residual stress field and the micro-damage field, and to characterize the uncertainty of the assessment result in the form of probability.

[0140] Generally, in this step, field reconstruction is first carried out. Each parameter vector sample in the solution ensemble obtained in S3 (where from 1 to ), is successively substituted back into the Karhunen-Loève (KL) expansion model established in S2. Through the KL inverse transformation, for each parameter vector sample a unique corresponding residual stress tensor field sample distributed over the entire computational domain and micro-damage field sample are reconstructed.

[0141] Specifically, after this reconstruction process, two sets of field samples are finally obtained, namely a solution ensemble of the stress field and a solution ensemble of the damage field . These two ensembles are the core achievements of the method of the present invention, and they represent a set of probability-weighted, possible "snapshots" of the true physical state inside the cladding layer.

[0142] In a possible implementation, point-by-point statistical analysis is performed on these two field ensembles to extract meaningful assessment information.

[0143] First, the posterior expectation field is calculated, which is considered the best point estimate of the true physical field. For the stress field, its posterior expectation is calculated by the formula:

[0144] ;

[0145] Similarly, the posterior expectation of the damage field is calculated by the formula:

[0146] ;

[0147] where is an arbitrary spatial position point in the computational domain, is the total number of samples in the solution ensemble.

[0148] Second, in order to quantify the uncertainty of the assessment result, the posterior variance field is calculated. For the damage field, its posterior variance at each point is calculated by the formula:

[0149] ;

[0150] The square root of the posterior variance field, i.e., the posterior standard deviation field, intuitively shows the spatial confidence distribution of the evaluation results. A region with a large standard deviation indicates a high uncertainty in the inversion result at that location, while a small standard deviation indicates a more reliable result.

[0151] As an option, this step also calculates the posterior probability distribution of one or more key quality indicators (KQIs). These KQIs are scalars that are of greater engineering concern and can directly reflect the service performance of the cladding layer.

[0152] In some embodiments, an important KQI is the peak tensile stress within the cladding layer . Its posterior probability distribution is obtained as follows: for each stress field sample in the ensemble , first calculate its first principal stress field within the entire computational domain , and then find the maximum positive value (tensile stress) in this principal stress field. In this way, each field sample corresponds to a peak tensile stress value . The set of these values forms the posterior probability distribution of the peak tensile stress.

[0153] Another important KQI can be the volume of the high-damage region . Its posterior probability distribution is obtained as follows: set a damage threshold , porosity 1%. For each damage field sample , calculate the volume of the region where its value is greater than . The set of these volume values forms the posterior probability distribution of the volume of the high-damage region.

[0154] In a possible implementation, based on the posterior probability distribution calculated above, the risk probability is calculated. The risk probability refers to the probability that a certain KQI exceeds its preset safety threshold. If it is stipulated in engineering that the peak tensile stress shall not exceed a certain critical value , then the risk probability of its exceeding the limit can be estimated by integrating or counting the posterior distribution:

[0155] ;

[0156] where is an indicator function that has a value of 1 when the condition is satisfied and 0 otherwise.

[0157] Finally, this step integrates all the analysis results to generate a detailed, visual, and probabilistic quality assessment report. Optionally, this report includes:

[0158] Three-dimensional color contour maps of the posterior expected stress field and damage field;

[0159] Three-dimensional color contour maps of the posterior uncertainty (standard deviation) field;

[0160] Histograms of the posterior probability distributions of the key quality indicators (KQIs), which may indicate their means, medians, and 95% confidence intervals;

[0161] A clear risk statement, "This assessment shows that the probability that the peak tensile stress of this cladding layer exceeds 200 MPa is 15% ± 2%", and "The probability of having a high damage area with a volume greater than 1 cubic millimeter is less than 1%".

[0162] In this way, the final output of the present invention is no longer a simple black-and-white "qualified" or "unqualified" judgment, but a content-rich and data-supported quantitative risk assessment report, providing a scientific and reliable basis for subsequent maintenance, repair, or usage decisions.

[0163] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the quality of a laser cladding layer of a water turbine, characterized in that Comprising the following steps: Obtain the ultrasonic waveform data of the laser cladding layer of the water turbine; Establish a joint posterior probability distribution that simultaneously includes a residual stress field and a microdamage field inside the cladding layer, wherein the joint posterior probability distribution correlates the residual stress field and the microdamage field with the ultrasonic waveform data through a forward physical operator that couples a nonlinear acoustoelastic model and a micromechanics model; Use a Markov chain Monte Carlo algorithm that utilizes gradient information to numerically sample the joint posterior probability distribution to obtain an ensemble of solutions for the residual stress field and the microdamage field; Perform statistical analysis on the ensemble of solutions to generate a probabilistic quality assessment result of the cladding layer that includes uncertainty quantification information.

2. The quality evaluation method of a laser cladding layer of a water turbine according to claim 1, wherein, The step of obtaining the ultrasonic waveform data of the laser cladding layer of the water turbine includes: Use an ultrasonic phased array probe to perform full matrix capture scanning on the area to be evaluated of the cladding layer to obtain a full matrix waveform data set.

3. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 1, characterized in that, Before establishing the joint posterior probability distribution, it further includes: Use the Karhunen–Loève expansion method to parameterize the residual stress field and the microdamage field into finite-dimensional random variable vectors respectively.

4. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 1, characterized in that The combined posterior probability distribution is determined by Bayes' theorem: ； wherein, is a vector of random variables characterizing the residual stress field and the micro damage field, is the acquired ultrasonic waveform data, is the likelihood function derived from the forward physical operator, is the prior probability distribution of the vector of random variables.

5. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 4, characterized in that, The forward physical operator takes the random variable vector as input, and its internal operations include: According to the above-mentioned reconstruct the residual stress field and the microscopic damage field; Apply the micromechanics model to calculate an equivalent elastic tensor based on the microdamage field; Apply the nonlinear acoustoelastic model to calculate an acoustoelastic tensor based on the equivalent elastic tensor and the residual stress field, and predict the ultrasonic waveform data accordingly.

6. The quality evaluation method of a laser cladding layer of a water turbine according to claim 5, characterized in that, The micromechanics model is the Mori–Tanaka model.

7. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 1, characterized in that, The Markov chain Monte Carlo algorithm that utilizes gradient information is the Hamiltonian Monte Carlo algorithm.

8. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 7, characterized in that, The gradient information of the joint posterior probability distribution required by the Hamiltonian Monte Carlo algorithm is calculated by establishing an adjoint state method solver for the forward physical operator.

9. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 1, characterized in that, The step of performing statistical analysis on the ensemble of solutions includes: Reconstruct multiple residual stress field samples and microdamage field samples from the ensemble of solutions; Calculate the posterior expectation field and posterior variance field of the residual stress field and the microdamage field, wherein the posterior variance field is used to quantify the uncertainty.

10. A method for evaluating the quality of a laser cladding layer of a water turbine according to claim 9, characterized in that, The statistical analysis further includes: Calculate the posterior probability distribution of at least one key quality indicator, and determine a risk probability that the key quality indicator exceeds a preset safety threshold according to this distribution.

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