Anomaly Detections for Manufacturing Systems Based on Sensor Data—Insights into Two Challenging Real-World Production Settings

sensors Article Anomaly Detections for Manufacturing Systems Based on Sensor Data—Insights into Two Challenging Real-World Production Settings Klaus Kammerer 1,* , Burkhard Hoppenstedt 1, Rüdiger Pryss 2, Steffen Stökler 3, Johannes Allgaier 4and Manfred Reichert 1 1Institute of Databases and Information System, University of Ulm, 89081 Ulm, Germany; [email protected] (B.H.); manfr[email protected] (M.R.) 2Institute of Clinical Epidemiology and Biometry, University of Würzburg, 97080 Würzburg, Germany; ruediger[email protected] 3Uhlmann Pac-Systeme GmbH & Co. KG, 88471 Laupheim, Germany; stoekler[email protected] 4ATR Software GmbH, 89231 Neu-Ulm, Germany; [email protected] *Correspondence: klaus.kammer[email protected] Received: 9 October 2019; Accepted: 2 December 2019; Published: 5 December 2019   Abstract: To build, run, and maintain reliable manufacturing machines, the condition of their components has to be continuously monitored. When following a fine-grained monitoring of these machines, challenges emerge pertaining to the (1) feeding procedure of large amounts of sensor data to downstream processing components and the (2) meaningful analysis of the produced data. Regarding the latter aspect, manifold purposes are addressed by practitioners and researchers. Two analyses of real-world datasets that were generated in production settings are discussed in this paper. More specifically, the analyses had the goals (1) to detect sensor data anomalies for further analyses of a pharma packaging scenario and (2) to predict unfavorable temperature values of a 3D printing machine environment. Based on the results of the analyses, it will be shown that a proper management of machines and their components in industrial manufacturing environments can be efficiently supported by the detection of anomalies. The latter shall help to support the technical evangelists of the production companies more properly. Keywords: anomaly detection; sensor data; machine learning; production machines 1. Introduction For manufacturing companies, the management of machine failures is becoming increasingly important. Due to the increasing complexity of the machines, downtimes of any kind can affect the overall success of a company. Buying a spare system is not an alternative solution as the acquisition costs normally surpass the benefit of the spare system. In addition, most replacement systems also require regular maintenance, even if they are not used. That is why companies are looking for new ways to manage machine failures cost-effectively. Predictive Maintenance is one topical subject, among others, which is a promising direction to tackle machine failures before they actually occur. However, the selection of appropriate techniques from the field of Predictive Maintenance is challenging as numerous aspects have to be considered [ 1 ]. In addition to Predictive Maintenance, there are many other approaches in this context for coping with machine failures such as Condition Monitoring or Continuous Improvements. Moreover, the trend towards machine learning raises the question of whether machine failures can be easily predicted. Although technical developments have improved the possibilities for manufacturing companies to cope with machine breakdowns, their practical application is still a challenging task for many reasons. On the basis of these considerations, the Sensors 2019,19, 5370; doi:10.3390/s19245370 www.mdpi.com/journal/sensors Sensors 2019,19, 5370 2 of 18 work at hand presents two real-world cases that were carried out in cooperation with manufacturing companies. For these companies, the detection of system errors is of utmost importance. In this context, it was shown that the detection of anomalies [ 2 ] of a machine is crucial for these companies. However, the meaningful detection of such anomalies is very complex. Interestingly, so far, many manufacturing companies often employ a selected choice of technical evangelists that are only able to detect anomalies based on their practical experiences over time. Such experts, in turn, are very expensive by design. To relieve them from manual decisions, this paper elaborates on how machine failures of these scenarios can be managed by analyzing sensor data of the production machines. In particular, the two examples will show that different types of sensor data, as well as detection techniques, should be considered. The first presented real-world setting is related to pharma packing machines. The latter machines wrap tablets into individual packaging units (i.e., blisters), and usually comprise several other components. For example, a product loader component pushes blisters and leaflets into cartons. This procedure, in turn, is prone to errors. Therefore, the packaging process needs to be continuously monitored to reduce costly downtimes as well as to comply with federal regulations. The continuous monitoring procedure, in turn, generates a large amount of sensor data coming from sensors that are related to the several components of the packaging machine. In addition, the pharma packing machine can be individualized for each customer, which might lead to many sensor parameter settings of the same machine type, including all obscured components. The second presented real-world setting is related to 3D printing machines in the field of optical products. In contrast to the first example, in the second setting, not only sensor values from the machine itself are important, but also sensors that measure the environment of the machine. Note that this fact distinguishes this scenario from the first one. Here, for example, an increase in the environmental temperature or humidity may have a significant influence on the production process of the manufacturing machine. Anomalies, such as room temperature that has negative effects on the machines, should, therefore, be avoided. Regarding the anomaly detection in general, plenty of algorithms were proposed that address different use cases [ 3 ]. The main objective of these algorithms is to analyze streaming data to develop models that can be used with an appropriate number of parameters and across applications, i.e., for machines with different characteristics and purposes. As in most practical cases, a very large number of sensor values must be analyzed simultaneously, detailed knowledge of the individual parameters is at least mostly of secondary importance. For manufacturers, anomaly detection algorithms with a minimum of parameter settings should be easy to apply and suitable for streaming analysis [ 4 ]. Consequently, this type of algorithms should feature mathematical operations with low computational complexity in order to minimize latency in long-running streaming analyses. Based on the two real-world examples and their different characteristics to predict anomalies for production machines, this work contributes to the following major insights (see also Figure 1): • For the pharma packaging machine scenario, sensor streaming data was evaluated with the goal to predict anomalies of one particular machine type. More precisely, machine-internal sensors (see Figure 1a) are acquired and their data is transmitted to a sensors data processing service. The latter then evaluates the sensor data with a distance profiling method (see Figure 1b). For this use case, it is shown that the requirement of efficient anomaly detection methods was found, which is also able to cope with the huge amount of sensor data of the analyzed packaging machine. Following this, the pharma packaging company can address other machine types as well. • For the 3D machine scenario, environmental sensor data was evaluated with the goal to predict anomalies that may affect the production machines. More precisely, temperature sensors (see Figure 1d) send data to a message broker via the Message Queuing Telemetry Transport protocol (MQTT) (see Figure 1c). A machine learning service (see Figure 1e) then predicts temperature values that may have negative effects. If a temperature anomaly is detected, the sensor data processing and the machine learning services notify a machine operator via a service message using the message broker. In this use case, several investigated machine learning approaches are Sensors 2019,19, 5370 3 of 18 presented, which had the goal to efficiently detect anomalies of temperature values. Furthermore, considerations on different sizes of training and test data are discussed. • For production companies, the detection of anomalies becomes increasingly import. As more research is required to get better insights into real-world scenarios and datasets, this works contributes with the results of two complex use cases. The selection of appropriate algorithms and their parameterization is still challenging, which can be also seen from the fact that less standard software is offered in this context. Broker Machine Machine Learning Service start/stop Machine Operator Environmental Sensors Sensor Data Processing Pipeline Internal Sensors b e a c d Machine Data Use Case Environmental Data Use Case Production Environment transmit environmental sensor data subscribe publish alerts transmit machine sensor data notify publish machine events Figure 1. Schematic overview of the presented use cases. The remainder of this paper is organized as follows. First, related works are discussed in Section 2. In Section 3, the method of distance profiling is applied to a real-world dataset of a pharma packaging machine, while Section 4shows methods to predict anomalies of environmental data of a 3D machine’s manufacturing room. Section 5discusses the results and deals with the revealed limitations. Section 6 concludes the work with a summary and outlook. 2. Related Work Regarding the acquisition of sensor data in manufacturing systems, which is an important prerequisite of this work, different related works exist. The authors of [ 5 ] discuss requirements for data acquisition of production systems and introduce an architecture based on the Open Platform Communications Unified Architecture (OPC UA) for data transmission and the precision time protocol (PTP) for time synchronization [ 6 ]. The authors of [ 7 ], in turn, provided an overview of methods, technologies, and exchange protocols to enable dynamic data acquisition of sensor data in industrial systems. Challenges regarding the representation and transformation of sensor data in cyber-physical systems are presented in [ 8 ]. In the field of semiconductor manufacturing, various case studies exist to improve manufacturing processes by analysing manufacturing sensor data [ 9 ]. Thus, Advanced Process Control (APC) methods utilize control strategies and analyses to identify machine faults and their causes [10]. The results are then used to, for example, optimize maintenance schedules [11,12]. In general, different anomaly detection techniques exist, which can be classified into statistical methods, such as Statistical Profiling [ 13 ], Parametric Statistical Modeling [ 14 ], and Machine Learning Approaches [15]. Concerning use cases of anomaly detection in industrial systems, the authors of [ 5 ] introduce a model-based approach for the prediction of energy consumption in production plants in order to detect anomalies using the ANODA algorithm [ 16 ]. [ 17 ] detected anomalies by applying a Bayesian network and scoring the resulting features according to a scoring model. The authors of [ 18 ], in turn, developed an assistance system for data acquisition, process monitoring, and anomaly detection in industrial and agricultural processes and evaluated three use cases. Anomaly detection was developed Sensors 2019,19, 5370 4 of 18 individually for each use case and is based, for example, also on the distance profiling approach, with a local outlier factor and PCA-based anomaly detection [19,20]. Regarding stream-based anomaly detection in general, different approaches exist. [ 21 ] conducted anomaly detection based on an auto-regressive, data-driven model of the considered data stream. They analyzed data streams of real-world wind speed measurements. The authors of [ 22 ], in turn, presented an approach based on half-space trees, which is a one-class anomaly detection algorithm. Its advantages with respect to the computational complexity are constant time and memory footprints. Finally, [ 23 ] introduced an anomaly detection method based on the Hierarchical Temporal Memory (HTM), which is a stream-based sequence memory algorithm. Furthermore, they introduced datasets containing real-world data streams with labeled anomalies to enable benchmarks for stream-based anomaly detection. For time series prediction , plenty of related works exist. In [ 24 ], an algorithm called Ultra Fast Forest Tree (UFFT) was investigated that examines the behavior of an ensemble of regression trees on streaming data. The work introduces a hybrid adaptive system for the induction of random forests from streaming data. The UFFT system is an incremental algorithm that poses a constant time complexity to process each instance, works online, and uses the Hoeffding bound to decide when a split test is installed on a leaf leading to a decision node [25]. The algorithm uses a continuous data stream and during the training phase, short-term memory is used. This method, in turn, is restricted to binary classification. However, it can be extended to a multiple classifier by increasing the number of classifiers and building a random forest of binary trees. Although UFFT is not better in prediction, it is significantly faster than the C4.5 algorithm [ 26 ]. However, UFFT is not able to detect little or abrupt concept drifts like [ 27 ], who investigated drift detection. They present an algorithm, which creates Regression Trees (RTs), instead of Random Forest Trees, based on data streams in the presence of concept drifts. RTs are faster in learning, but are prone to outliers, as they do not work as an ensemble. The Fast Incremental Regression Tree-Drift Detection (FIRT-DD) algorithm allows for model adoption at any time and is able to deal with local concept drifts and adapts locally. By doing so, global model adoption is avoided to gain efficiency. The change detection algorithm is based on change detection units (CDUs) that monitor the growing process. CDUs require few memory spaces per node and a small, constant amount of time complexity for each sample. Ref. [ 27 ] defined concept drifts as a change of the underlying joint probability, i.e., a change of P(Y|X) , and distinguished between three main approaches of concept drifts: (1) methods that explicitly detect concept drifts, (2) methods that use ensembles of decision models, and, (3) methods that are based on data management using a sliding window (similar to our presented approach). Fast Incremental Model Trees with Drift Detections (FIMT-DD), the successor of FIRT-DD, is based on randomized model trees and combines them to ensembles, which leads to a random forest regression [ 28 ]. Each leaf and node of a tree is built on randomly and independently chosen attributes. The authors additionally created an Online Regression Forest (ORF), i.e., out of ten FIMT-DD, with a tree depth of five. However, there is no striking outperformance of one of the presented algorithms when comparing a single online tree, including optional splits with a random forest consisting of ten trees [ 29 ]. While performance, in general, depends on the dataset, empirical analyses showed that a single online option trees with averaging fits best for most compared datasets. Altogether, the combination of (1) how anomaly detection methods have been integrated into technical settings of real-world examples of production machines and (2) application examples of how anomaly detection of sensor data can be performed in a data-driven manner, without major parameter optimizations, has not been presented by the discussed other works so far as done in this paper. 3. Pharma Packing Use Case—Machine Sensor Data The following use case presents the application of distance profiling to a real-life dataset of a pharma packaging machine with the goal to detect anomalies of a machine component. In the first step, relevant sensor data was collected. Then, the obtained sensor data were processed by a data processing pipeline. Sensors 2019,19, 5370 5 of 18 Practical results show that distance profiling can be a valuable method to detect the anomalies of the pharma packaging machine components. Use Case Description: Uhlmann Pac-Systeme GmbH & Co. KG is a mechanical engineering company headquartered in Laupheim, Germany. Uhlmann is a supplier for pharmaceutical wrapping packaging machines. The blister machines of Uhlmann put tablets into individual packaging units. For example, the offered machines form blisters with individual courts for tablets from a plastic or aluminum foil strand (see Figure 2). Tablets, in turn, are fed and sorted into blister courts. The latter are completed with a cover sheet, while finished blisters are finally punched out by the Uhlmann machines. Figure 2. Uhlmann blister machine B1440i. As all Uhlmann packaging machines are used in the pharmaceutical industry, country-specific laws and regulations must be considered and fulfilled. These legal requirements are related to the validation of machines, including the provision of detailed documentation of all process steps that are performed during drug packaging. Notably, every packaging machine delivers sensor data, which can be continuously monitored in order to detect anomalies. As an important preliminary technical step for the detection of anomalies, the acquisition of sensor data and the generation of actuator signals must be provided by programmable logic controllers (PLC) [ 30 ]. Along with the example of a product loader, this preliminary step will be shortly delineated, as it shows the characterization of the resulting sensor data. The product loader station of an Uhlmann blister machine loads blisters and leaflets into a carton. The product loader consists of several sensors and servomotors. Specifically, two functional assemblies with servomotors are running in parallel, while the sensors of each single servomotor generate four signals that represent the 1. mechanical position (MP) of the assembly (ProductLoader.Position), 2. the difference of a reference value and the actual value of the MP (ProductLoader.Dref), 3. the power consumption of the assembly (ProductLoader.Current), 4. and the reference signal of the assembly (ProductLoader.Reference). Overall, eight signals per product loader can be acquired. The physical process of product loading and product releasing is executed in continuous cycles. Note that the packaging performance of a machine is therefore expressed in cycles per minute. During these cycles, different anomalies may occur. A machine component can lock, which leads to a production halt. This can be caused, in turn, by a faulty feeding of the packaging box. Furthermore, wear and tear of the ball bearings can lead to increased frictional resistance or a complete failure of the ball bearing lubrication. Both anomalies are reported by the technical evangelists to be detectable by analyzing the power consumption of the product loader. Fundamentals: To detect anomalies in time series data, distance profiling can be applied [ 31 ]. A distance profile, in turn, is a vector D of the Euclidean distances between a given time series pattern pand every possible subsequence siin the respective time series s(see Figure 3). Sensors 2019,19, 5370 6 of 18 Pattern p Subsequence nm Distance Profile D= Time Series s dp,1 dp,2 dp,3 dp,n-m+1 sn-m+1 ... Figure 3. Distance profile for a signal. In this paper, Mueen’s Algorithm for Similarity Search (MASS) was used to calculate the distance profile [ 32 ]. When calculating the distance profile, the resulting time complexity is O(nm) . MASS uses a convolution-based method to calculate the distance profile of a pattern in O(n×log n) . Furthermore, a z-normalization is applied to the generated distance profile vector during the calculation as well. If the Euclidean distance between a pattern p and a subsequence si is smaller than the value of a threshold, then p and si are considered to be similar. Sensor Data Acquisition: When processing sensor data of the pharma packing machines, different steps have to be performed [ 33 ]. First, sensor data has to be collected from a PLC and transferred to a collection component. We developed a binary transmission protocol to transfer sensor data directly from the PLC to a collection component via TCP sockets. The protocol offers different frame types for time synchronization, signal metadata description, and sensor data point transmission. Sensor Data Processing: The transferred raw data stream has to be split into windows and pre-processed if it features disturbing noise. After the pre-processing step, the data is processed through fast-Fourier transformations and finally stored if no further processing steps are required. In this step, we adjusted the already existing technical development to enable the integration of anomaly detection approaches after the pre-processing step. To enable this, the utilized processing pipeline must provide a high variability for every sensor signal, which means that the pipeline is generally difficult to manage and configure. To address these issues, we have developed a Sensor Data Processing (SDP) framework in C# of Microsoft. NET for collecting, processing, storing, and visualizing raw sensor data in a continuous processing chain, according to the data stream processing model [ 34 ]. The SDP defines a graph-based processing model, in which processing nodes are connected to each other to handle all aforementioned and required pipeline steps in a controlled way (see Figure 4). Figure 4. Schema of the sensor data processing pipeline. Sensor Data Analysis: The dataset used in this work was generated by an Uhlmann endurance test arrangement in the Uhlmann technical center in Laupheim, Germany. To be more specific, an isolated product loader station was running in a continuous operation mode. For our practical evaluation, sensor data were collected over 10 days by the SDP and stored in a MongoDB database. In total, 1,127,790 timestamps per signal (i.e., time synchronization frames) and 18,736,022,320 data points (i.e., floating-point numbers representing the measured sensor data) were recorded during the mentioned time period, including NULL values for the signal gaps. In terms of disk space, the recorded values correspond to roughly 22 GB. Further note that the dataset comprises a few signal gaps due to connectivity losses between the PLC and the storage component. Importantly, the dataset contained records of bearing damage, which eventually led to the failure of the machine. Apart from that, the dataset can be considered as being healthy, as the endurance test and an evaluation of the log Sensors 2019,19, 5370 7 of 18 data generated by the test execution system showed no other abnormalities. Figure 5shows the mechanical position and power consumption values of five arbitrary product loader cycles ( x1 to x5 ) of the considered dataset. During a cycle, the mechanical position values increase monotonously, while a product is loaded into a carton (x-axis). The power consumption (y-axis) shows positive values if the product loader is increasing in its speed, while negative values show breaking actions. When a new cycle starts, the position is set back to zero. Figure 5. Power consumption (blue) and reference signal (orange) of an assembly. Distance Profiling: For this practical use case, the SDP processing pipeline was adjusted by changing the receiver node to receive BMTT data, a windowing node (see below), and a processing node implementing the distance profiling based on the MASS, and an output node to publish MASS results to a broker (see Figures 1c and 4). A pre-processing node is not necessary as the MASS processing node calculates z-normalization and distance profiles simultaneously. As the SDP pipeline processes data streams, windowing had to be applied [ 34 ]. Therefore, correlation windows are used. The latter are a specialization of session windows [ 35 ]. In contrast to session windows, correlation windows are triggered by one event at the beginning of a new window. In the SDP, correlation windows may be also generated based on other signals. Here, a window trigger is executed based on the master encoder, represented by a saw-tooth signal (see Figure 5). That means, the regular clocking of the master encoder (about 720° ) was used to divide the related signals into uniform windows by detecting its falling slope (dataFrame.position[i+1] - dataFrame.position[i]) <− 500). The MASS algorithm was then applied to the data of the power consumption signal of the product loader, as it offers the most expressiveness of the mechanical process and features a very high resolution, i.e., one data point per 2 milliseconds. In contrast, the mechanical position offers only about 1000 different, monotonously increasing values (see Figure 5). Moreover, a comparison between the individual patterns becomes possible. Therefore, a new counter value is created for each recognized new pattern of a window. In order to classify a new pattern, the Euclidean Distance is used to determine the signals of existing patterns with the signals of new patterns. In practice, the counter value increases rapidly at the beginning of an analysis series, as well as in the range of any anomaly and drops below a certain limit thereafter. Note that the number of patterns caused by detected anomalies are gradually considered “normal” by MASS, and are therefore smoothed. Conversely, this means that after a large number of detected patterns, it is not assumed that the anomaly has been disappeared. Results: On the given 10-days dataset, the application of the MASS with the developed SDP processing node took a total run time of 60 min. As a result, the MASS detected fewer than 5 patterns per Sensors 2019,19, 5370 8 of 18 data point analysis after 22 h in the dataset, i.e., the baseline was reached. Interestingly, about 14 h prior to bearing damage, the number of detected patterns increased rapidly (see Figure 6). At 10:00 a.m., the number of detected patterns returned to 1 pattern per sample. At 01:30 p.m., the number of detected patterns increased again to 7, whereas at 01:48 p.m., the machine finally stopped working due to bearing damage. Figure 7a shows window-layered plots of the power consumption in the normal condition (few detected patterns), whereas Figure 7b in bad condition (many detected patterns). The x-axis represents the reference signal of the product loader in degree, while the y-axis represents the actual power consumption in milliampere (mA) of the two assemblies. In Figure 7b, power consumption shows a higher variance. Interestingly, the idle phase shows the highest variance for power consumption. One reason for this may be the control loop used as during slow movements, the actual position is approached to the reference position with smaller speed changes,. A higher variance also means a lower motor precision of the movements in the normal state. Figure 6. Number of detected patterns (y-Axis) and time (x-Axis) of a product loader of the last 14 h collected. Figure 7. Phase folded plot of ( a ) normal situation with less detected patterns and ( b ) a detected anomaly with many patterns. Summary: The dataset of the product loader component of a pharma packaging machine was analyzed to detect anomalies in the collected dataset. The selection of a proper anomaly detection algorithm is challenging as many variants of a machine exist and the selection of parameters for Sensors 2019,19, 5370 9 of 18 each machine requires high efforts. Therefore, the development of a parameterless algorithm that fits into the setting of the pharma packaging machine should be a major goal. In this paper, a distance profile anomaly detection algorithm was presented and applied. Specifically, the distance profile was calculated with the MASS based on the z-Euclidean Distance. The latter offers various advantages, e.g., it requires few parameters. For the sensor data acquisition, the developed sensor data processing framework (SDP) was used. The latter is based on a processing pipeline model that is configurable and extensible, i.e., other anomaly detection algorithms can be flexibly integrated. Although it is a rather simple method, MASS showed promising results on the presented real-world dataset. It was possible to detect anomalies in a meaningful manner, i.e., based on the number of detected patterns, 13 h as well as 18 min before the damage. Practically, this means that a technical evangelist of the pharma packaging company can better analyze the data to decide whether bearing damage can be avoided by stopping the machine or replacing components before damage actually occurs. However, it has also been shown that the integration of the anomaly detection method requires considerable technical efforts. 4. 3D Printing Machine—Temperature Environment Data The following use case presents the application of prediction models to a real-life dataset of a measuring room of 3D printing machines with the goal to predict anomalies of temperature values. In the first step, relevant sensor data were collected. Then, the obtained sensor data are processed and promising features are selected. Finally, machine learning models predict upcoming values and warn technical machine operators about possible anomalies. Use Case Description: An industrial company in the field of 3D production machines operates a measuring room equipped with nine temperature sensors and additional sensors for air humidity (%), air pressure (mBar), and airflow (m/s). The room contains an arbitrary number of machines and their operators enter and leave the room at arbitrary points in time. Machines within the room are allowed to operate within a temperature threshold, which is defined individually for each machine. A temperature control unit tries to keep the temperature in the room between the upper and lower threshold. The challenge of this project is to figure out temperature anomalies for the measuring room that is solely based on the provided environmental data and does not contain any contextual information of the operated machines, such as the number of operators or the actual number of the machines in the room. Furthermore, no standards for acceptable errors were set for the project. The models presented below return a prediction error on a basis for which the technical evangelists can decide after a notification whether the error rate is acceptable or not. Sensor Data Acquisition: The measuring room is sending the current sensor information with a transmission rate of one value per 3 min. Figure 8illustrates the used architecture. Hereby, all values are combined using the JavaScript Object Notation (JSON). Next, all sent messages are transferred via the Message Queuing Telemetry Transport protocol (MQTT), which is a publish/subscribe based message protocol for machine-to-machine (M2M) communication. The machine learning code is implemented as a separate service using the scikit-learn python library [ 36 ]. The scikit service subscribes to the environmental values and uses them to train a machine learning model. The model is constantly evaluated and, whenever the predicted temperature value exceeds a defined threshold, the responsible machine operators (i.e., the technical evangelists) are alarmed. In contrast to the first use case, here, the integration of the anomaly detection method is technically easier. However, the selection of proper algorithms is more challenging than for the first use case. Sensors 2019,19, 5370 16 of 18 min_samples_split=2, min_weight_fraction_leaf =0.0 , presort=False , random_state=0, s p l i t t e r = ’ best ’ ) MLPRegressor ( a cti v at ion = ’ relu ’ , alpha =0.0001 , batch_size= ’ auto ’ , beta_1 =0.9 , beta_2 =0.999 , early_stopping=False , ep si lon =1e −08, hidden_layer_sizes =(100 ,) , learning_rate= ’ constant ’ , l e a r n i n g _ r a t e _ i n i t =0. 001 , max_iter =200 , momentum=0.9 , n_iter_no_change =10 , nesterovs_momentum=True , power_t =0.5 , random_state=None , sh u ff l e=True , solver= ’ l bfgs ’ , t o l = 0.0001 , va li d a t i o n _ fr ac ti o n =0.1 , verbose=True , warm_start=False ) RandomForestRegressor ( bootstrap=True , c r i t e r i o n = ’mse ’ , max_depth=10 , max_features= ’ auto ’ , max_leaf_nodes=None , min_impurity_decrease =0.0 , min_impurity_split=None, min_samples_leaf =1 , min_samples_split=2, min_weight_fraction_leaf =0.0 , n_estimators =1000 , n_jobs=−1, oob_score=False , random_state=1, verbose =0 , warm_start=False ) References 1. 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